At that point, it simply became a Starfleet tradition for all Federation starships named Enterprise to carry the NCC-1701 registry, IMO. The lettered suffixes are there to just signify each subsequent ship to do so. It's a small acknowledgment of Starfleet history and is totally harmless.^^^ Right, maintaining tradition and history is fine.
And by using the name Enterprise again and again, that honors all the prior famous vessels so named (seagoing and otherwise). And it works for Lexington, Intrepid, Constellation, Yorktown, etc.
But by using the registry #-suffix, it only references a SPECIFIC Enterprise, again and again and again, rather than all the other historic Enterprises.
I say...one time is sufficient. After that, still continue to use the name Enterprise, but with a new registry. That would imply a tradition of ALL Enterprises again, rather than that ONE previous Enterprise.
You make sense, the second Constitution Class 1701-A with Captain Kirk should have been the only one, then the GENERATIONS Excelsior Class Enterprise needed a new registry number without the B.
I hope the tradition continues for another century or two...