X standing for eXperimental is nice speculation - but IMHO it's even more natural to speculate that it stands for eXploration.
After all, Archer's ship was indicated to be Starfleet's first ship designed for deep space exploration. (Not much point building exploration vessels if they don't have engines capable of moving them outside already explored space! And "already explored space" would have expanded by a leap when Earthlings "allied" themselves with Vulcan; most of it would simply be space explored by Vulcans, too far out to be reached by humans until Henry Archer's superengine came about.) And in naval tradition, the letters before the number specify ship type
, that is, the ship's intended mission, rather than its class or model.
So, NX-01 is the first-ever Starfleet eXploration vessel, and belongs to the Enterprise
class. Since there are not other eXploration vessels in existence, everybody can also refer to this as the NX class (just like everybody could call the Ticonderoga
class the AEGIS class, and did, until other designs also got equipped with AEGIS). At some point, further exploration ship classes are no doubt designed, and it would become confusing to refer to all of them as "the NX class", so Starfleet (and later UFP Starfleet) reverts to speaking of the Enterprise
class and its successors...
...Thereby perhaps explaining why the UFP Starfleet never has seen it fit to build an Enterprise
class of starships. The name has already been used up!
Why the pennant letters would cease to specify ship type at that point, and would start only denoting the ship's operating organization (NCC=Starfleet ship), we don't know yet. But apparently the model switches from "Earth naval" to "Earth aeronautical", where the letter prefix indeed indicates nationality.