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.
I don't think we have any continuity demonstrating the Enterprise C was a/the flagship, but that being said, consider the extreme amount of time between the Enterprise C and Enterprise D (relatively speaking), there was certainly other flagships.
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).
Anywhoo, less I digress; it would make sense to me if registry numbers had some sort of further significance beyond NCC. For instance, maybe the starting of the number might designate other purposes too. This would be a whole ton easier to swallow if the USS Defiant, USS Voyager and USS Equinox had different numbers.
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.