I don't like the Yorktown idea because we already saw a commander and assuming he had a crew in command of the ship during the Probe crisis. What? Did that commander get thrown off his own ship just to make Kirk happy?
For all we know, the original Yorktown
captain and crew were reassigned to a new Excelsior-class ship with that name. In that sense, what Kirk got was a hand-me-down ship renamed Enterprise
as a PR move to the Federation public and the rest of the Galaxy at large.