ST precedent was with the Excelsior as NX-2000, experimental vessel. When Excelsior later went into service, we see NCC-2000. Makes sense.
Then we see Enterprise as NX-01, using the NX again to denote experimental vessel. Fair enough, new warp five engine and all that.
But then the Enterprise goes into service for Star Fleet, it should have been become NCC-01. It was no longer serving as an experimental vessel, it was being put into service on missions.
This was the United Earth Starfleet, not the Federation Starfleet -- it should no more be expected to use the same nomenclature than one should expect the Massachusetts State Navy to use that of the United States Navy, or than one would expect the Royal Scots Navy to use that of the U.K. Royal Navy.
I would have liked an entirely different registry setup. Maybe "SWF" for "Space Warp Five," to designate that she has an entirely different engine than earlier Earth ships, the same way the Navy uses "CVN" to denote nuclear-powered aircraft carriers.
I also would have preferred a different prefix rather than no prefix: "UES" for "United Earth Starship." So in the world according to Sci, maybe it would have been the UES Enterprise