Here's a thought that's been running about my head since the 80s. With Constitution class ships being made up of two hulls, the saucer being identified as the main hull, if the the main hull is attached to a new drive section, does it get or deserve a new hull number? I think it could go either way.
Yes, this goes back to a theory on the Constellation NCC-1017 being something other then a Constitution class ship, yet similar enough, when first launched and then refited into being a Constitution class later on.
Any thoughts on this old chestnut?
I think that the Constellation is a Constitution class ship and always was, because that was the original intent of the episode. Fanwank theories about the ship being a different class based solely on the registry number or the minute differences between the studio model and the model kit is roughly analogous to making a mountain out of a molehill.
REAL answer - it was a quick-and-dirty "fix" job. I would have reordered the digits ("1710") when doing the CGI reworking a while back, if I had been in charge. The reason for the odd number was to prevent people from seeing it and thinking it was the Enterprise, even if they had a fuzzy, static-filled screen. NOT an issue, from my perspective, today.
Now... as for an "in-universe" explanation?
I've heard stories about the other ships having different registry numbers, out of the 17xx sequence, but I've never really cared about that because we never saw a Constitution-class ship, on-screen, with numbers assigned, except for the Enterprise and the Constellation... did we?
If we need to treat the Constellation as really being 1017, well... it just seems obvious that the number was a "reassignment."
See, I don't see the NCC as standing for "Naval Construction Contract." I see it as standing for "navigational contact code"... basically, an enhanced IFF signal.
After all, we have various ships, later on, which carry forward the 1701 contact code, although we know that they weren't build under the original construction contract, or any "addendum" to that contract... right? Each of them pulses out "1701" as the ship's contact code...
SO... there was some famous, history-making starship called the Constellation, and the Constitution-class was named (and numbered) to honor that original ship. Since the earlier ship was MUCH earlier, there was never any issue of the two being confused... so they just reused the code as-is.
Later on, the destruction of the rebuilt Enterprise (which retained virtually nothing except for the code transponder from the original ship!) resulted in another ship being given the name "Enterprise." (And, as far as I'm concerned, it wasn't an already-operating ship which, after years in service, was renamed... it was clearly a new-built ship, though it may have been built with the INTENTION of being christened something else.) Because that ship was very similar to the previous, they had to modify the code slightly... adding another character, basically.
But the Constellation was just named and numbered to honor a previous "hero ship" (which we've just never, yet, heard about!)