Nothing necessarily states that the civilian government and Starfleet were on the same page here. Kirk ended up making Starfleet look rather incompetent about the whole Genesis affair. That had to have ruffled some feathers with the higher ups.
If Starfleet wanted to punish Kirk, they would have just drummed him out of the service, not given him a (admittedly malfunctioning) ship and sent him on a mission.
If you think about some of the COs we see in the movies -- Terrell who ignored a missing planet, Styles with hubris befitting the worst of Greek tragedies, Esteban who would report in to request permission to move his bowels, or nervous Harriman who left dock with half his ship missing -- Would you want one of them taking on a mission of any great importance?
Those are four captains. I believe Starfleet has more captains than that. Perhaps even one that might even be competent enough to fly in, beam up some hostages, and fly away again.
We can forget by the time the movies come up that Kirk is a diplomat too and a veteran one. Enterprise is a prestigious ship. The Enterprise was sent because you can't screw about kidnapping Federation diplomats.
By the time of the TMP movies, the original Enterprise was a cadet training ship. And in the context of the TOS movies as a whole, the Ent-A seemed to be just a toy given to Kirk to play with temporarily until the new Ent-B was built. None of that screams "prestigious" to me.