This would explain why a new ship of an older design would be built while its successor was undergoing trials.
Personally, I disbelieve in both aspects. Rather than being built, NCC-1701-A was probably just renamed, with minimal effort. If we believe that she was created for Kirk, then it wouldn't make sense to cobble together a cluster of spares at great expense when either of the two alternatives - giving Kirk a proper, modern ship and giving Kirk a nostalgic leftover vessel no other skipper would agree to fly any longer - would be so much more cost-effective. And if we believe she was created for Starfleet, it wouldn't make much sense to waste time and money in building an outdated design, even if the spares existed for doing so. (If starships were as expensive as space shuttles, relatively speaking, there wouldn't be a Starfleet!)
And rather than being a designated successor to the Constitution
class, the Excelsior
was probably its own thing... Real successors would probably already be in service, perhaps for their second decade or something, considering how outdated the Enterprise
was already considered to be.