I figured someone would bring up the point of the USS Enterprise having linage purpose for maintaining the number, but the thing is, the Enterprise B wasn't a/the flagship of the Federation. At the time of the Enterprise B's launch, the Excelsior was the flagship. It wasn't till years down the road that the Enterprise B was appointed as a flagship.
There is no indication that the Excelsior was ever Starfleet's flagship. Given the big media event the launch of the Enterprise B was it would have to have been the flagship. Or do all the Federation's news reporters attend the launch of every starship?
Oh that point, in DS9 and later in novels, we start to form an understanding that a flagship isn't necessarily the flagship of the entire federation fleet, but rather the flagship of it's particular fleet. If I am not mistaken, the Enterprise D/E was the flagship of the 7th Fleet or 9th Fleet (opinions seems to differ).
DS9 never did this, indeed the Enterprise D was referred to by Odo as the flagship of the Federation in Bar Association. The novels have these days suggested this interpretation as a means of being more realistic.
The other thing that tends to hurt my head when talking registry numbers and there is a TON of overlap with names too. A great example is the Saratoga was shown as both a Reliant Class and Nebula Class in very short order. It's potentially believable but hard to swallow.
Huh? In all Star Trek, there have been four Saratogas:
mentioned as the previous assignment of one of Trip's engineers in Enterprise.
-The Miranda class ship
seen in the opening of Trek IV.
-The other Miranda class ship
Sisko served on in the opening scene of Emissary.
of unknown design mentioned in TNG's sixth season and DS9's sixth season.
There has never been a Nebula class Saratoga.