Here’s my theory for the Enterprise-A:
During STIII, Morrow mentions that the Enterprise is to be decommissioned. What he doesn’t say is that it’s because a new Enterprise-A is being planned, an Excelsior class ship. But because of the events of STIV, Kirk was awarded another Constitution class ship like his old one, and it was named the Enterprise-A in his honor (and the fact that the original Excelsior class Ent-A wasn’t finished being built yet), so instead the ship builders made the Excelsior class the Enterprise-B, and Kirk was just given command of the A temporarily until the B was commissioned. That’s why the A was decommissioned so soon after it’s construction: it was time for the B to be christened. The A was probably recommissioned after that with a new name and registry number.
During STIII, Morrow mentions that the Enterprise is to be decommissioned. What he doesn’t say is that it’s because a new Enterprise-A is being planned, an Excelsior class ship. But because of the events of STIV, Kirk was awarded another Constitution class ship like his old one, and it was named the Enterprise-A in his honor (and the fact that the original Excelsior class Ent-A wasn’t finished being built yet), so instead the ship builders made the Excelsior class the Enterprise-B, and Kirk was just given command of the A temporarily until the B was commissioned. That’s why the A was decommissioned so soon after it’s construction: it was time for the B to be christened. The A was probably recommissioned after that with a new name and registry number.