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.
Tell that to Captain Sisko and his USS Defiant NX-74205. And then his replacement Defiant also numbered NX-74205.
But seriously, Enterprise NX-01 was NX-class, just like the Botany Bay was DY-class (as C.E. Evans
pointed out) and the Horizon was J-class. Perhaps "NX-" being used as an experimental registry was a tribute to the first Starship Enterprise and her sister ships.
Or maybe they just wanted a big "X" on the hull 'coz it was kewl.