It would just mean we would all have to accept that for some unknown period of time every single person at that particular shipyard just spontaneously forgot how to build a working starship...
Hmm...
You know, I'm liking your "old ship quickly pushed back into service" idea more now...
They wouldn't have to forget how to build a starship, they'd just have to forget how to build that particular class. The Boeing plant in St. Louis is still cranking out F-15s and F/A-18s, but I wouldn't count on anyone there still knowing how to build an F-4, at least not without a lot of defects.
Given the incredible amount of standardization and automation present in design install, do you really believe that so much difference existed (shell design notwithstanding) between classes? The Enterprise A wasn't built as an experimental design- StarFleet had been (and continued to build) the C-Class Heavy Cruiser for a long, long time along with its internal components.
The only rational explanation for the way the A behaved out of spacedock was that SOMEONE... or perhaps a lot of someones... were drunk at the assembly station.
My take has always been that there were unexpected incompatabilities between the new modules and the old ones. Think about it. The Enterprise we (briefly) see launching at the end of
Star Trek IV looks substantiviely different internally than it does in
Star Trek V and
VI (the latter case looks different to
V as well, but only cosmetically so IMO). Now, evidently the bridge module
at the very least has been replaced, perhaps because Starfleet think if they're gonna have a new Connie out there, then it had better be updated to a level comparable to the Excelsior class ships they intend to populate the fleet with. So, the bridge module (and probably various other plug-in components throughout the ship) is one of the new designs intended for this fleet of upcoming Excelsiors, but it's been crudely installed into the Constitution architecture which slightly rejects it, and that's why we get these rampant malfunctions all the way throughout
Star Trek V.
Basically, a bit more time would have sorted everything out, but Admiral Bennett
insisted that the 1701-A had to go on the Nimbus mission for God knows what reason (Get it? "God" knows? Hey?
Star Trek V? Okay, okay, don't explain the joke Lance

), so they had to launch her, whether the ship was actually in working order or not. Even Kirk felt the need to point out how ridiculous that was, but you know, orders are orders.