the actual Yorktown was in the same movie and likely had a full crew aboard
I don't see how that would be relevant. If Starfleet wants to give the ship to Kirk, it tells the previous batch of officers to fuck off and Kirk to sit down. That's simply how it works.
...Except perhaps in Starfleet, where starship crews appear to train for long missions as a single team, astronaut-style (see McCoy's comments about the training going on at the start of ST2). But that wouldn't change much, either: Starfleet would then simply tell the previous officers and
crew to fuck off and have Kirk and
his crew sit down.