Why risk one of their best captains and crews on a rescue of useless ambassadors,that was the question?
PR stunt would be my guess, since it should have been a milk run. They could have sent anything that held air and warped to the planet and just beamed everybody up if it weren't for the ship, which brings me to my version of your risk question ...
Why risk one of their best captains and crews on a ship that would probably demonstrate the lemon law is alive and well in the 23rd century is a better question. Do they want these guys to croak?
(the 'only ship in quadrant' scene in TFF includes Bennett saying he needs Jim Kirk, to which Shat does the 'oh please.' to me it is played at the audience as much as the guy on the viewscreen.)