No reason the Starfleet of the 29th century can't have an alternate system of registries that include a letter with the first vessel to bear the name.
While we could rationalize it that way, I think it's more a case of someone forgetting that A would be placed on the registry of the second Relativity, not the first.
With the Relativity's unique mission, those letters could even designate alternate versions of the ship.
Cool idea... As for the Enterprise letters, the E-A appeared to be a unique ship in Starfleet history in being a deliberate replica of a previous vessel. The whole point of giving this ship to the man who saved Earth (again) was to give him a personal memento and trophy (and a ship that turned out to be a completely expendable lemon, perhaps not coincidentally). Bureaucrats couldn't allow for two ships to carry the same registry, of course, so NCC-1701-A was the next best thing... We might very well argue that the E-A was the first UFP Starfleet ship with an -A suffix, at least, if not the only one. The -B in the E-B might have been a pure publicity trick, just like having Kirk aboard for the launch. The Cold War had just ended - surely Starfleet needed all the good PR it could get in launching a massive new starship! Two ships would then create a pattern Starfleet would be disinterested in breaking. For the Yamato to be at -E when the Enterprise is still a -D isn't a wonder, considering the big gap between the E-C and the E-D... Timo Saloniemi
Yes, that's probably the real life reason behind it. "In-Universe", however, I think it had been intended as a psychological message to the Romulans, who had suffered plenty of humiliation from the Enterprise NCC-1701. Would also explain why the Romulans in TNG were constantly eager to get their hands on yet another Enterprise. The name of the ship and its registry must be something like a red flag for any Romulan. Bob
Then again, in ST4 the big enemies were still the Klingons. Why insult an enemy's enemy? Timo Saloniemi
That makes since. I don't know much about the Enterprise B besides it being a modified Excelsior-class but it's advancement may have been planned to be the best at what it does of it's time deeming it worthy of calling it Enterprise. The same with the heavy cruiser, Ambassador-class, war time ship that C was. The D was a flag ship that saved earth multiple times and the E was also the most advanced ship of it's time. Maybe the Enterprise label means it's the best they have?
This is curious... We have the Saratoga NCC 1887 which we saw in Trek 4, disabled by the whale probe. Then we saw Sisko's Saratoga get blowed up by the Borg in Emissary. I always figured that it was meant to be the same ship from Trek 4, but the registry number is different (NCC-31911). And then we have the ship apparently built to replace Sisko's one, which docked at DS9 in "Wrongs Darker than Death or Night." Assuming that these were the only ships to bear the name Saratoga, I would have thought Sisko's one would have been the Saratoga A.
Actually, it was still 74205. The reason they didn't change it was because they couldn't justify changing the registry for only a few episodes and re-doing all of their ship shots. If they'd changed it to 74633, then they could have changed it just as easily to 74205-A.