Argthtjtr

In the approach phase, engine 1 of Cathay Pacific flight 780 got stuck at about 70% N1 and it forced the crew to do an overspeed landing (230knots).

Why didn't they shut it off by turning the fuel pumps off? Is there a backup mechanism if the fuel valve fails like in this scenario?

You can find the full incident report here and this topic is touched upon briefly, but in short they had little to no time to entertain any other options but a full speed landing.

It was not until the aircraft [was] on the final descent for landing that
the Commander realised they could not reduce the thrust on the number
1 engine. The speed was not controllable and from that point, there
was no time for the crew to consider other strategy nor procedure to
cope with such emergency situation.

and more in the conclusion section...

t. At that stage, there was no time for the flight crew to consider other
strategy nor procedure to cope with such emergency situation. The
flight crew concentrated on flying the aircraft for a safe landing.

First off, the engine was throwing errors throughout the flight and they were talking to the maintenance team at other points. Ultimately, the proper steps were taken and everything was done by the book. They were prepared for an engine-out landing. When you have a runaway engine malfunction (or throttle stuck at full) shutting down prior to landing may not be the right decision if the running engine provides no immediate safety risk. If you shut down a problematic engine in flight you run the serious risk of not being able to get it started again.

Considering that most airports have a bit (or a lot) of extra runway, EMAS systems and often land at the end of the runway, coming in overspeed and burning through your tires and brakes may be safer than cutting the engine and potentially falling short of the runway.

Engine #2 wasn't doing its job either

Had the situation just been engine #1 stuck at high thrust, with engine 2 normally controllable, than what you describe would be a reasonable response to the situation. However, that was not the case with CX780 -- during approach, Engine #2 was stuck at 17% N1 (or rather below idle) and thus delivering effectively nil thrust.

As a result, the pilots dared not shut down engine #1 until they were safely stopped on the ground.

From the incident report section 1.1.4:

a. At 0519 hrs during the descent to a cleared level of FL230, ECAM
messages “ENG 1 CTL SYS FAULT” and “ENG 2 STALL” were annunciated
within a short period of time. According to the Commander, a light
“pop” sound was heard and some “ozone” and “burning” smell was
detected shortly before the ECAM message “ENG 2 STALL”

Then later:

e. At 0530 hrs, when the aircraft was approximately 45 nm southeast
from VHHH and was about to level off at 8,000 ft AMSL, ECAM message
“ENG 1 STALL” was annunciated.

So now both engines are out, they started the APU and successfully managed to restart #1:

h. The crew moved the thrust levers to check the engine control but
there was no direct response from the engines. The No. 1 engine speed
eventually increased to about 74% N1 with the No. 1 thrust lever in
the CLB (climb) detent position. The No. 2 engine speed remained at
sub-idle about 17% N1, with the No. 2 t hrust lever at the IDLE
position.

Engine 2 was out of action, producing no power, engine 1 had failed, but was temporarily working although they couldn't adjust power, if they'd shut that down too they'd have been gliding and probably would have crashed with total loss of life. They didn't have the power to climb and had one shot at landing, so they made damn sure they got it on the runway, not a bad landing considering the circumstances.

On a humorous note, another example of pilot understatement:

l. At 0539 hrs, the Commander made another PA advising the passengers
of having “small problem with the engines” with small vibrations and
requesting them to remain seated and follow the directions from the
cabin crew.

Aside from what Unrec. and GdD point out, even if the other engine had been running perfectly...

A frequent problem with twin engine airplanes is shutting down the wrong engine. Nobody ever expects or plans to shut down the wrong engine, but it happens anyway.

So a crew is very cautious to shutdown an engine that is working.