I guess the only thing to add here is that we probably agree the letter part of the registry would be an utter waste of paint unless there were alternatives to NCC. That is, yes, we know that there exist registries such as NAR-something and NSP-something etc., and yes, we have good reason to think that these correspond to the operating organization of the vessel in question, leaving NCC the specific "Starfleet operates me" symbol. But this further carries the connotation that a pairing
of letter identifier and string of numbers would be unique, so it's possible that the strings of numbers alone
need not be unique.
See what I mean? There may exist both NCC-12345 and NAR-12345 within the same system, these being separate ships. But OTOH, there might not
If, for clarity, a registry already used for a NCC vessel never gets used for a NAR or NSP one, then the number of actual Starfleet ships goes way down. Starfleet might be the leading "consumer of registries", but it might also come a distant second to some other organization, at least at certain periods of UFP history.
Do we have any canonical cases of the same number being used with two different letter prefices?