FYI on aircraft registry numbers N is the designation for USA and X is for experimental thus Charles Linberg’s “Spirit of St Louis” is NX-211. I suspect the NX-01 is a homage to Linberg’s plane and keeping with Trek tradition of NCC and NX which appeared on Sisko’s Defiant.
That’s the convention by the 24th century (and maybe even by Kirk’s time), but who knows if that convention has been developed yet? So far, Enterprise is Starfleet’s only starship, so there’s really no need to have “classes” – there’d only be one calss with one member, so why put the extra line on the form?
Starfleet has plenty of ships. It has only one starship. Any ship that can fly through space is a spaceship. But a starship is something else again. It’s a term that refers to ships that move very fast, fast enough to get from one inhabited world to another within days or even hours, not months. (Contrast this with Ensign Mayweather’s dad’s long-haul freighter.) These ships are sent out into the wide galaxy in the continuing effort to explore strange new worlds, etc., and are Earth’s first ambassadors as well as her canaries in the mineshaft. It takes a special kind of man to captain a starship, someone with both a sense of wonder and a backbone of iron. And while captaining a spaceship is no mean feat, it’s orders of magnitude less than taking a ship out into space where nothing is known except that there’s a new danger waiting every week.
The distinction, BTW, was first noted in the TOS episode The Doomsday Machine.
Well, the USS Enterprise is an Enterprise-class ship, and it’s the only ship of its class. Clearly the “Name of first ship in class-class” tradition goes back to way before the Enterprise (NX-01). And, while Starfleet might not bother with a “class” of ship if they only had one ship, period, I think they definitely would want a “class” given that they have various ships, but only one Warp-5-capable starship, just as the U.S. Navy had a new class for its first (and, for some years, only) nuclear-propelled aircraft carrier.