The most valuable person for flying the shuttle would be the person with the most experience and skill not "everyone". I find the idea that everyone on the shuttle "is trained to fly and fix the shuttle." a bit dubious. This is the Enterprise with a crew of over 400 not the ISS, the Space Shuttle or Apollo where a very small crew needs cross training. The shuttle was out for a "three hour tour" with the specialists needed for observing the quasar.I think it depends on how you define 'most valuable'. When it comes to flying a shuttle, why is Spock more or less valuable than the others? Scotty is the engineer, Boma is a scientist, and everyone on board is trained to fly and fix the shuttle.
Spock has a better chance of surviving on the planet than the others and is heavier due to his physiology. It might be deemed more logical for him stay.