Argthtjtr

A firstborn donkey must be redeemed by giving a lamb or goat kid to a kohen. If the owner of the donkey doesn't redeem it, the donkey must be decapitated with an ax and buried.

Rashi says that this is a punishment: By refusing to perform pidyon peter chamor, the owner caused a loss to the kohen, and incurs a loss himself.

But it's also similar to chalitza: the phrasing is "if he doesn't want to". And there's no problem choosing chalitza over yibbum: some say it's more important because nowadays people can't have proper Kavana when doing Yibbum, and in practice Ashkenazim almost always do chalitza.

So, lechatchila, can the owner of the donkey choose to break the donkey's neck rather than redeem it?

The Rambam (Hil. Bikkurim 12:1) writes:

מצות עשה לפדות כל אדם מישראל פטר חמור בשה ואם לא רצה לפדותו מצות עשה
לעורפו שנאמר ופטר חמור תפדה בשה ואם לא תפדה וערפתו ושתי מצות אלו
נוהגות בכל מקום ובכל זמן ומצות פדייה קודמת למצות עריפה:

It is a positive commandment for every Jewish man to redeem the first
[male] issue of a donkey with a seh. If he does not desire to redeem
it, it is a mitzvah for him to behead it, as [Exodus 13:13] states:
"The first issue of a donkey you shall redeem with a seh. If you do
not redeem it, you shall decapitate it."

These two mitzvot apply in all places and at all times. The mitzvah
of redemption takes precedence over the mitzvah of beheading [the
donkey].

According to the Rambam, one fulfills a mitzvah by beheading, but redeeming has preference (and this parallels yibum and chalitzah). However, Raavad (ibid.) takes issue with Rambam's formulation:

ואם לא רצה לפדותו מצות עשה לעורפו. א"א בחיי ראשי אין זה מן הפלפול ולא
מן הדעת המיושבת שיחשוב זה במצות עשה אע"פ שאמרו מצות פדייה קודמת
למצות עריפה לא שתחשב מצוה אבל היא עבירה ומזיק נקרא ומפסיד ממונו של
כהן ומפני שאמר מצות פדייה אמר מצות עריפה

According to Raavad, one who beheads the donkey has committed a sin, destroyed property and caused a loss to the kohen. Although the Mishnah refers to the "mitzvah" of arifah, this is only because it has already referred to the mitzvah of pediyah, but arifah is not a mitzvah at all.

Mishna Bekhorot 1:7

מצות פדייה קודמת למצות עריפה, שנאמר "אם לא תפדה וערפתו"‏

The Mitzva of redeeming precedes the Mitzva of [killing], as it says "And if you don't redeem is, [kill] it".

So the owner could choose to kill it, but that's not what he's supposed to do. This is actually just like Yibbum, as the Mishna continues to explain, at least in cases where Yibbum can be performed with proper intention (which some communities assume is not common nowadays).

(I don't know if you should call that "lechatchila" or not.)