We're already in that territory anyway when Decker says, "This is an almost totally new Enterprise." My head-canon is rooted from what I see. There's nothing from the Enterprise in TMP, TWOK, in TSFS that looks remotely like it did in TOS.I'm not sure melting the TOS Enterprise down to its raw materials and then rebuilding the TMP Enterprise from scratch using them really counts as "refitting"; if anything I'd say that was more "recycling". And such a drastic reuse of the TOS Enterprise's raw materials really stretches credibility that it's the same ship in any meaningful sense. Certainly not to the point that you can justify it having the same registry number.
I think keeping it NCC-1701 was a political move.
With the Titan-A, which supposedly was built out of the previous Titan, they changed the registry number. They retrofitted Discovery and changed the registry number there too. So, I think what happened with the Titan and the Discovery is more typical of what Starfleet does with registry numbers but, for PR reasons, they just didn't with the TMP Enterprise.