As I mentioned before, I respectfully disagree, as there had been 15 continuous years (or 21 if you don’t consider series overlap) and 526 episodes of TNG, DS9, and VOY where the registry scheme for ships was pretty much consistent throughout that entire time, because the same people were in charge of stuff like that; people who actually cared about minutiae like this and painstakingly documented it in notes and official publications. It wasn’t the scriptwriters’ job to come up with registry numbers for ships; it was the art department and VFX personnel.
As for LDS, I get the impression that the wildly inconsistent registries for the California class ships aren’t because of some perceived notion of arbitrariness that didn’t actually exist. I think they’re just meant to be in-jokes that the audience doesn’t know or care about.
Based on the evidence from 1966 onward, that doesn’t seem to be the case, at least not until the 32nd century of DSC season 4, where future Starfleet went from 6-digit NCC numbers back to 4-digits.
