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?
Actually, some in Starfleet Command would probably answer "YES!" It was only a short time ago, remember, that Kirk basically humiliated the entire Admiralty (and made a mockery of the whole SF rulebook) by his actions in ST II & III. They had to honor the Federation Council's wishes by giving him a ship, but that didn't mean they were happy about it - or that they would just let it go. (Or that they had to give him a top-of-the-line ship, for that matter.) You didn't think Kirk & Company's retirement five years later was voluntary
, did you? The brass had to save face somehow. "Maintaining discipline in rank" and all that...