There was a ship called Enterprise, then it's blown up. So its crew are assigned a new ship.
Nope - the ship is blown up, and her top officers
are assigned a new ship.
Basically never happens in the real world; crews don't get to hold together like that, not even small groups of top officers. But here we were rather explicitly shown that the troupe was transferred as a package because they were public heroes who deserved a reward. And part of that reward appeared to be that Starfleet agreed to paint a new name on a starship.
In reality, ships don't get successors, not in the one-on-one sense. And ships certainly don't get replaced by new ships of the same name. Not in military tradition, and not for military reasons. But everything here fits well with the concept of a PR stunt, which then overrides all other considerations and negates the value of evidence.