Why didn’t the Captain of Cathay Pacific flight 780 shut down engine 1 and land with a more reasonable speed?
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.