While inexperience of the crew and battle damage were definitely issues, I don't think that was the driving factor behind the crew reassignments. Rather, the Enterprise and her crew were considered damaged goods politically.
I still say that has nothing to do with it, because they were
not "the crew." They were Academy cadets assigned to the ship for a single training flight. Basically it was a field trip. Their experience or the political situation had nothing to do with it; they were just never
meant to be aboard the ship for longer than that one training mission. And the training cruise was a birthday outing for Admiral Kirk, which suggests that it was intended to be just a day long. So getting diverted to Regula I and getting their butts kicked by Khan made them all very, very late for their next classes.
We never know the full extent of the fallout from this. Several of the aliens present in the federation council in TVH were missing from the Khitomer Accords in TUC. Perhaps some member worlds chose to part ways with the Federation in the intervening time. The overmining that cause explosion at Praxis may have occurred in direct response by the Klingons to this event.
Is there any reason that every member world would need to be represented? Maybe it was just the worlds with a stake in the question of detente with the Klingons, e.g. those near the border or those that would need to provide resources for rescuing Qo'noS's ecosystem.
The revelation that Starfleet had chosen to dispatch a desk-bound maverick has-been on training vessel crewed by cadets -- who then chose to personally assume command and then screw up so bad that it's Captain had to sacrifice his life so that all souls wouldn't be lost - for such a sensitive project probably did not instill much confidence in the current leadership of Starfleet in question.
The idea of Kirk as a "maverick" is a myth that arises almost entirely from his behavior in
The Search for Spock, which hadn't happened yet. Watch TOS and you'll see he's anything but a maverick. He's a serious, disciplined officer who takes his duties and obligations seriously, who usually obeys direct orders even when he dislikes them. What's often misinterpreted as defying authority is actually
exercising his own authority as the commander on the scene to determine how the laws should be interpreted, something that frontier captains are
supposed to do by virtue of their position. And what's often misinterpreted as Kirk "violating" the Prime Directive is actually upholding it by its 23rd-century definition -- he intervenes to cancel out other sources of intervention like Klingon spies, crazy Federation captains and historians, and evil computers, thereby freeing cultures to pursue self-determination thereafter.
The only times in Kirk's onscreen career that he blatantly disobeyed direct orders were in "Amok Time" and
The Search for Spock -- in both cases, placing Spock's life above his duty. The rest of the time, he took his oaths quite seriously.