I wish they hadn't gone out of their way in "Relics" to explicitly point out "there have been five starships" with the name Enterprise. Later retconned to be five Federation starships named Enterprise (as of when "Relics" takes place). Even though it made for a great gag.
Now the fact that they went 85 years without a Starship Enterprise (2161-2245) looks weird, given everything else we've seen. And given how Starfleet likes to recycle names. There's room for a good three or four post-ENT/pre-TOS Enterprises. It's just that Kirk's became the most famous. And he saved Earth twice (TMP and TVH). So the next Enterprise he was given had the -A attached to the NCC-1701. That's how I would've done it.
Now the fact that they went 85 years without a Starship Enterprise (2161-2245) looks weird, given everything else we've seen. And given how Starfleet likes to recycle names. There's room for a good three or four post-ENT/pre-TOS Enterprises. It's just that Kirk's became the most famous. And he saved Earth twice (TMP and TVH). So the next Enterprise he was given had the -A attached to the NCC-1701. That's how I would've done it.