On reflection, I've come to see the 1701-A as having been a kind of 'provisional ship', a intermediate and completely unplanned for step that Starfleet took only because of the exceptional circumstances with the Earth probe in STIV. This might also help explain why (mistaken registry of the USS Yamato aside), we never see another Starship carry over a previous registry number with a prefix.
Here's the timeline as I see it:
In STIII, Admiral Morrow says the Enterprise is to be mothballed, and while we aren't shown it, he probably also clues Kirk in on the Excelsior program and the plans for a new Enterprise while he's at it. Due to the thing with Spock's katra, Kirk and crew steal the 1701, blow it up over genesis, get Spock back, and are exiled to Vulcan. When they return to Earth, save it from the whale probe, and the various theories about needing to punish Kirk but also (outwardly) reward him see him and crew being assigned to an unplanned Enterprise: given the registry 1701-A to indicate its kind of "unofficial" status. Kirk and crew are then effectively off active duties, although they are occasionally reunited and sent off on special missions together where their unique expertise is advantageous (Nimbus III, convoy for the Klingon chancellor). Enterprise-B is under active construction by this point, so when the call comes through that Starfleet wants to recall 1701-A, it isn't entirely a surprise to the crew: they've all been effectively off 'active duty' for a while anyway, and the newer Excelsior Class Starship Enterprise is probably very much a known quantity by then. The decision is also taken to use the registry 1701-B for the new ship (as a nod to the unique legacy of the Enterprise -- maybe before the Earth probe saga it would have been launched with a different registry number somewhere in the 2000s), something which becomes a tradition for all the subsequent ones as well.
What do we think? It seems like a plausible chain of events to me.