Except that it's explicitly called an NX-class starship -- that is its proper name.
So the proper name of the DS9 hero ship is "Escort-class"? Or that of the Klingon ST3 design "Scout-class"?
Neither of those were called "Escort-class" or "Scout-class." The NX-class was called "NX-class," multiple times. The meaning is clear: The United Earth Starfleet, at least part of the time, used a different naming scheme for its ship classes than the Federation Starfleet later did.
Starfleet may very well refer to the ship as NX-class, but that doesn't mean there wouldn't be a more systematic way of referring to it, too.
And yet there is no evidence that it has any other name.
all I am saying is that UE Starfleet in the 2150s is more likely than not to call the NX class "Enterprise class" as well, because they also speak of "Neptune class", Triton class" and possibly "Daedalus class".
There is no evidence that that is the case. The evidence we have is that the NX-class is called the NX-class, period.
I see no particular reason the Daedalus class can't be akin to the B-52 Stratofortress in that regard.
Especially if Daedalus and Enterprise represent different ship categories altogether - like B-52 and F-117 do.
Well, the thing to remember about the F-117 is, as I understand, that it was really a bomber, but it was deliberately mislabeled as a fighter rather than a bomber in order to attract fighter pilots. Hence it being called the F-117 instead of the B-117.