They reproduce like cicadas.

Some small creatures take their time about reproducing. Some cicadas take 17 years to reach sexual maturity. That's more time than larger creatures such as dogs and cats.

Your fairies may reach sexual maturity only after they are 40 or 50 years old.

And then, like cicadas and so many other insects, they mate, lay eggs and die, all within just a few days.

That would make the loss of fairy life more dangerous to them as a species than the loss of a human life is to us. They will want to play cool with other races.

Flying creatures have a much higher metabolism for their size, especially non-gliding kinds like fairies. If you assume they have a metabolism similar to a hummingbird, then a 10 pound fairy will need just as much food as a full grown man; so, scarcity would be just as meaningful if not more so to them because not only do they need just as much food, but they will need to stop to eat more often because of their smaller stomachs and lesser body fat.

Aside from this fact, (since you asked for an answer that does not involve eating a lot for their size), what constitutes as a fair fight may be relative. Their speed and agility may give them the opportunity to out maneuver a giant warhammer for a quick slash to the neck, but their advantages may have well-known counters such as using nets, flails, water hoses, specialized armor, or other weapons & techniques that make it an uneven fight.

Basically, other races can adapt their methods to kill lightwings much more easily than the inverse; so, while they may do well in the opening days of a conflict, an enemy that is prepared to fight them will typically win, even if outnumbered.

1. Transhumanism runes are no longer available.

If you and your family were hungry, and had the opportunity to change yourself such that you all would not be so hungry, probably you would do it. You are right that after the Fall lots of people would want to be Lightwings. But after the Fall (or at some point before) the Transhuman runes are no longer available. The Lightwings that already exist will not increase in number - there is no way to do it. Except possibly by breeding...

2. Lightwings have no inherent affiliation with other Lightwings.

If I am Latvian in the US, and somehow Latvians have a survival edge after the Fall, I will find other Latvians. For one, I go to church with a bunch of them. I have been to their houses. For two they speak and read Latvian. I can put up signs. Also there is a restaurant we all used to go to and so I would recognize them if I saw them. They think like me, we have a shared background, we can talk and we get along. We can definitely team up.

Your Lightwings are raised human. Their families are human and their background is their human background. The only thing I as a Lightwing have in common with other Lightwings is that at the time Lightwing bodies were on offer, I thought they looked cool and I thought I would try it out. I chose Lightwings because I have always been hot for Tinkerbell but maybe it turns out that a vast majority of people who chose to be Lightwings chose that because they were old and aching and very heavy and were tired of it. These old folks qua Lightwings like to complain and argue, and voice their suspicions about what kind of people the other Lightwings were before they were Lightwings. They are not much for the teaming up.

My buddies, on the other hand, are a bunch of other things besides Lightwings. In once sense that is a shame because there is no Tinkerbell equivalent, but otherwise it works well. It is easier hanging with them because they are not fussy old jerks and actually our strengths complement each other.

Lightwings taste really good. Like, really really good. Finger-licking, marrow-sucking good. While they hold their own one-on-one against the general population, there is a rare subspecies that specializes in hunting/trapping lightwings (after all, what lightwing can resist delicious bluebell pollen). Lightwings need to stay hidden to avoid capture. Large population centers of lightwings are like a smorgasbord for trolls.

Some brave lightwings use a glamour to hide their identity while wandering in plain sight. Tales of their gruesome demise when revealed are well-known.

Kleiber's law and Square-Cube Law

You say they eat less than a human, but...

The Kleiber's law states that the metabolic rate of organism scales at 3/4 power of their mass.

The Square-Cube law states that each time you x2 the radius of an object, you x4 the surface, and x8 the volume.

A human weight 110 lb and has 5 ft of height. A fairy has 1 ft. That is five times the size, or $5^2 = 25$ the volume, which is linearly related to mass. A fairy would weight $110 / 25 = 4,4 text{ lb}$. If the metabolic rate of an human is 2,000 calories, the metabolic rate of a fairy would be $(2,000 / 110^frac{3}{4}) times 4.4^frac{3}{4} = 178 text{ kcal}$.

A human needs $frac{2,000 text{ kcal}}{110 text{ lb}} = 18 text{ kcal/lb}$ while a fairy needs $frac{178 text{ kcal}}{4.4 text{ lb}} = 40 text{ kcal/lb}$, they need more calories per the same abount of body mass.

What means all that? It means that the relation of food mass / body mass is higher on fairies, so they are much more vulnerable to dehydration, malnourishment and starvation. They are able to survive much fewer days without food or water, due they has a higher metabolic rate in proportion to their size, and so they can carry less fat in their own body.

Little Offspring

Fairies grow and develop much slower compared to a human. Despite their size, they need much more years to mature, and when they do, they breed less often than humans does (less fertile or actives?).

Fragile

Fairies are much fragile than humans. They are much more fragile towards sickness, cold, hot, hunger, wounds, diseases, etc.

By the way, fairy medicine isn't so advanced as human medicine, they are a quite new race. Even more, maybe fairies need a much stricter diet due to their fragile bodies.

Predation

We need to qualify your statement, a fight between a lightwing and a human of equal skill and equipment would be a fair fight. The problem is this: what kept the lightwings from overwhelming humanity before the apocalypse? It had to be something. So, let's talk about why they're an equal match.

Let's talk about flies.

Flies suck. They buzz around your head. You swat them with your hand and it it doesn't phase them. You grab a fly swatter and you can only kill them (unless you're lucky) when they land somewhere and wait for death. It's a good thing flies are dumb as rocks or they would have overwhelmed humanity a long, long time ago.

Except that humans discovered aerosol poison. And ultraviolet light (but this isn't as important).

Now, ignoring the fact that aerosol poisons would work against lightwings as well as flies, the point I'm making is that the lightwing's advantage is small-mass and high-speed. The human's advantage is strength. Since they're both intelligent, one would hope that's a wash (although the gas fields of WWI proved that intelligence on both sides doesn't always avoid death. Aerosol poison is a real problem for you).

But this doesn't mean there aren't predators. Making the lightwings godlike is bad for your story. Another statement you made is this: an individual lightwing is a match for any other creature. The reality is: they absolutely cannot be (or they would have overrun the humans a long, long time ago).

You know what lightwings have problems with? Hawks and other birds of prey. Sure, they're smart enough to use swords. They might even have magic. Hey, maybe they have mini AK-47s. But when swift and mighty death is approaching you at a bazillion miles an hour from the heights of heaven and you don't know it....

Predation

They eat things that humans do not, and that is as scarce as human food. You could make them reliant on some shared resource but have others be completely separate if you want to give them a reason to fight (they both drink water, but eat totally incompatible foods, for example).

This doesn't solve the living space issues - lightwings could fit in smaller spaces, but fighting over their scarce food means they isolate themselves into smaller groups. They may also need some special environment to be comfortable and happy. Humans like to be out of the weather and somewhere around 70 degrees. Maybe lightwings need very high humidity, or they can't handle extreme temperatures. Those examples might limit their range too much for your story, but some other acceptable requirement could limit their ability to congregate in large numbers but still allow them to live in various locations/environments.

Because lightwings are solitary creatures. To the point of being unable to exist with other lightwings unless it's mating season.

They explode.

You move one lightwing to another one and closer they get they start to magically vibrate and when they touch they resonate with each other channelling their inner magic on the same oscilloscopy level of recipient and it make them explode.

Also ancient curse. Modern curse. that one rune that make them die. and that spell that make more than three lightwings on square meter turn into hotdogs.

Having just watched the scene in The Matrix, where Agent Smith describes how humanity is the only 'mammal' seemingly incapable of establishing an equilibrium with its surroundings, the only answer so far is that, that is just not their way. Otherwise this answer will quickly dissolve into reasons against the statement that humans have not established an equilibrium (oh, no... we're running out of oil. Again).

On the face of it your question seems story based, but it's actually one of logistics; as all good questions are. Native Americans had respect for their land, because they had respect for the generations that would come after them. It's simple sound logic. But what compels a culture to comply is a question for the ages ... or a damn history book.

You should watch Wizards

The answer to that one is pretty simple - fairies are stupid.

Look - they are 1 foot tall. So on average (assuming human proportions), compared to a 6 foot tall, 200 pound person, they weigh something like 1 pound. That, in turn, suggests a brain weight on the order of 1/4 ounce. How smart can such a being be?

Even if you assume a brain which is 10 times larger than human (proportionate to body mass) you're only up to about 2 1/2 ounces.

Furthermore, fairies will need significant investment in brain tissue to control their wings, which will reduce the "spare" brain capacity required to do abstract thinking.

Nosajimiki's answer is definitely the most significant. Maybe they don't need as much food - but they need to spend a massive proportion of their time eating in order to maintain that lightweight metabolism.

Nosajimiki has missed a lot of the other consequences though. Unless they have some supplemental magic to help, a 5oz fairy cannot carry a 1lb coconut. Not even if they grip it by the husk...

Basically, anything involving moving, lifting or pushing stuff is going to be beyond them. They can't drive. They can't operate most machinery. They certainly can't carry any weapon larger than a poisoned needle, and they can't wear any armour, protective clothing, gas masks, or anything else heavier than gauze. Operating computers should be OK, with a suitable keyboard and mouse - but they may need help to push it into a USB socket against the connector retention spring. They would have a huge advantage for some assembly work such as fine-pitch soldering, but they would never be able to use a screwdriver or spanner, or to move the circuit board themselves.

So lightwings can certainly find a role in society, but there's an awful lot they can't do.

For an example of small and large fairy creatures coexisting in a semi-modern environment, read Tad Williams' War of the Flowers. It's a pretty good book anyway.

Being big (like us) helps when the winter comes, the mass grows faster then the radiating surfaces. Your tinkerbells are too small, they mass-surface relation will kill them when the temperature falls. Also, they have wings and wings are basically radiators. They will spend most of their time eating sugary foods and drinking water to keep their body hot enough for them to live, like hummingbirds.

Also, being so small they won't be able to access some of our sources of sugar - they won't grind cereals, nor milk cows. Fires will be dangerous for them. Flames that would just hurt our fingers with 2nd degree burns will burn their internal organs because they don't have enough mass protecting their liver and heart and brains from fire's heat, they are too small.

They would have to live like sentient hummingbirds: will have to domesticate new plants and animals to get their sugary diet and will be restricted to the tropics. Domestication takes time and until they can somehow create on their own plantations of flowers full of sugary nectar and domesticate those ants that have a sugar reservoir on their abdomen, like some brazillian ants (I belive China has a similar ant species) they will live a miserable life.

Also, predation and competition. If you are 1 foot tall, cats, dogs, birds, rats, some insects and snakes change from pets to predators. And in the niche of eating sugar, bees will compete with you. A full-sized human can stand a lot of bee stings because we are too big and our skin too hard. Your tinkerbells won't. A bee sting in their abdomen will get right into the liver and the bee's venom will kill them.

So, they won't rule the world, they will live a miserable existence hunting for sugar, attacking bee's nests in deadly battles and hiding from one of the most lethal predators the earth has ever seen - the cats, both feral and domestic. I hope they chose well the other five runes.

It doesn't matter

It doesn't matter why faeries can't form super swarms, because if 1 faerie can come anywhere close to handling a single human in combat, then a troop of faeries is going to utterly destroy an equally sized group of humans if they put their mind to it.

How?

Guerrilla warfare.

There just aren't any practical ways to defend a camp from a group of small, intelligent, flying intruders. There will be faeries in the food. Faeries in the sleeping bags. Your shoes will go missing, your nets will have holes, and all the buttons will mysteriously vanish. Unless the humans have an underground bunker with an airlock, they're utterly screwed if the faeries decide they want the humans dead. Even with an airlock, I wouldn't put it past a determined faerie to be able to sneak inside.

If your fairies retain their intelligence then there aren't many options actually

Arrogance

Simple enough. Because of how easy it is for them to survive and flourish(as compared to non-fairies), they begin to believe the world belongs to them, all the more so when you consider their numbers. In other words, they develop a sense of manifest destiny. They don't go around in large swarms mainly because they see no need/can't be bothered to organize themselves sufficiently. Hostile encounters between fairies and non-fairies tend to be in small groups or even one on one because of a twisted sense of honour, which is probably just a veneer for sadism.

You say they require less resources because they are tiny yet still are equal in a fight with a human. But why wouldnt you just say "they might be tiny but still use similar amount of food and water as humans"? Give them an ability for eating a lot in a short amount of time to shut people up about "tiny mouths=needs to eat most of the day" and you are done.

They need less food and water, but they are more sensitive to pollution of various kinds. Which is why they abandoned the neighbourhood of human beings and dwelled by preference in glades deep in the forests.

So, there are lots of areas where humans may thrive, but fairies can't abide.

They are less fertile than humans

Like in they have a really hard time having little fairies. This resource is used in Eragon's elves: they live very long (immortal unless killed) and they are way stronger (in everything) than humans. How to balance the species? Make it difficult to them to have kids. Like in extremely difficult: in their visit to the biggest elf city it's said they only have 2 infants iirc (read this a long time ago).

You probably don't need to make it that difficult, but it's an easy resource to balance species.

Also you can make it so they take longer to mature, meaning they are child fairies a longer time, slowing the rate at which they can create a big army.

EDIT: you can use the same resource the other way around to balance other species that are dumber/weaker/more prone to war/whatever.. just make them extremely fertile.

Calcium deficiency

Lightwings' zippy flight patterns are fine for soft tissues, but the high G-forces wreak havoc on their bones. Thus, these creatures require relatively very high levels of calcium intake. In fact, they reward other species younglings which leave calcium-rich teeth out for the fairies to collect.

It turns out that this need for calcium is the fairies' biological limiting factor. There can only be so many fairies as their are younglings to leave calcium deposits for them.

They're fascinated by bright lights, hence the name.

If your humans can survive the night, they'll find the entire Lightwing army staring stupidly at the sun, which is when most predators hunt for them.

They are way less social than humans, large lightwing villages have around 20-30 individuals, whereas the smallest human communities typically, bands, range from 20-50 individuals. The typical human community in your setting are tribes with ~150 individuals.

An individual human and an individual lightwing are evenly matched, but a human community and a lightwing community are not, in most cases lightwings are at serious disadvantage.

This is not hard to achieve, if lightwings are less trusting, and only tend to congregate as immediate family they can't form the large groups humans can.

Alternatively if you still want to be somewhat social, their magic start to interfere with each other. If you get to many living to close their magic stops working, or at least becomes more and more unpredictable and problematic. So a lightwing family may be fine IN a large human community, but a large community of lightwings turns into a huge fight, or more likely it is so disruptive they immediately split into smaller communities.

The easiest way is to limit their diet. Maybe they can only eat fruit (which goes bad rapidly and is more scarce in winter), or any one particular type of food. Maybe they can only eat raw meat, for instance, forcing them to hunt and making food storage essentially useless (but making a large sized rat a veritable feast). Even with lower-than-a-hummingbird metabolisms, restricted food sources could make being one less attractive.

Or you could limit them other ways. Such as, they don't eat at all but subsist off dew and sunlight (legends of fairies have suggested they once did). If that's the case then periods of dryness or dark could be very weakening to them. That would be a major factor in choosing to stay a lightwing, especially with only 7 days to become used to it. If night times forced a person to seek cover and hide because the longer the night went on the weaker they'd get, well, a lot of people wouldn't be happy with that sort of trade-off, no matter what power they had by day.

To someone used to always being strong, suddenly feeling great weakness would be a disorienting and frightening feeling, especially especially for someone who's sole focus is survival. Seven days isn't really enough time to get used to or adapt to such a thing either, so quite a number of people might Nope right out of their trial period and never look back.

Another limiting factor could be language--maybe lightwings speak only their own language and must relearn the dominant language, and even then may never speak it very well. This would mean families and friends may not be able to speak to one another, and that could be heavy factor in deciding.

Also, never underestimate "peer pressure." Choosing a form also means choosing other things. If a husband wants to be a lightwing but the wife wants to be an elf, they have a decision to make--separate as a couple or choose another form (unless they don't like sex). Or say the couple is fine with it but their child is stubbornly set on being an orc--how does a lightwing raise an orc? Or if all a child's friends are orcs, will they want to remain a lightwing? In this form they may rule at hide and seek, but they'll certainly never be part of a baseball game. Those sorts of peer group and familial pressures may drive a lot of people from the choice.

The desire to breed may be more of a social construct and less determined by environmental factors. A study living in a mouse utopia where the population was observed to collapse despite an abundance of food and space, even after the population had returned to previous numbers of successful growth, eventually continuing to fall until they all died out.

https://www.youtube.com/watch?v=5m7X-1V9nOs

One argument may be that due to the long-life and societal age of the fae races has led to a breakdown in the social behavior needed to grow a population.

A real-life parallel (although with entirely different factors) can be seen in Japan where the annual birthrate has fallen to the lowest in history and is continuing to decline, despite an abundance of wealth, food, prosperity, and relative safety from invaders as they have no immediate neighbors due to being an island nation.

It's interesting to try and speculate based on the obvious factors but both research and observation has shown that this is only a partial factor of population growth. Take the mcguffin of your choice and run with it. Sometimes the mundane can prove more interesting to the reader than a definitive reason. For example, you can take a failed study of your choice where certain unknown factors exist that lead to a collapse, providing similar parallels in your story, only to be understood by those familiar with such studies on societal collapse.

Dating is hard in the apocalypse

Sure they don't require as many resources to survive, but I'm assuming there's no more Tinder/OKCupid/etc in your apocalypse world, nor will there be fertility clinics/sperm banks/etc... Finding a life mate is hard enough even w/ all of the modern day resources available to us. After the fall populations are naturally going to be lower, and spread out more. And probably not a ton of people switched (assuming the option to do so was pre-apoc). If anything, any fantasy-race aside from humans is going to have a hard time maintaining a viable population increase unless their breeding cycle is much quicker.

Intraspecies bonding

Having once been human, there's a good chance your lightwings will still fall in love with humans, and vice versa. Especially if small groups have better survival odds in the wilderness cross-species teams will likely develop, including non-platonic relations (nevermind they won't be able to produce offspring).

The End of the world is no place to raise a baby

Many people (regardless of body form) will choose to forego children just because surviving the apocalypse requires so much resources that could be spent surviving. Add to this that since Lightwings are new, figuring out how everything works might not be an easy task. Even if they've got access to books, there's not likely to be any literature on their reproductive situation, nor on child rearing and there are probably vast differences in how a lightwing baby is raised from how a human one is. In fact some "expected" handling of lightwing babies may end up being lethal or injurious.

Lightwings get cancer really easily. Much more easily than humans. (Kind of the opposite of elephants who only rarely get cancer.) Since the apocalypse involved lots of radioactive things being splashed around, your Lightwings can only visit and live in very constrained areas. They can't even eat bananas. So you get little clusters of Lightwings living in the really nice, pristine areas, surrounded by species who are less vulnerable, but the outside species can't push in because the Lightwings out-breed them, and the Lightwings can't push out because of the radiation...and you get conflict on the borders.