Question: Why wasn't the NX-01 Enterprise ever mentioned in the later times, or added to the count of the starships named Enterprise?
Answer: Because it was there all the time, since the dawn of the series.
Here's my take on the history from 2151 to 2285. Not to be taken too seriously, of course.
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The only reason that I can see as appropriate is simply the fact that NX-01 was pre federation and starfleet, 1701 was not, but that would not satisfy the reasons for the shuttle enterprise and the carrier enterprise being shown in model cases or pictures. actual reason is probably simply one of continuity not being able to be applied backwards if you suddenly decide to make a show set in the past and add to that history in ways not covered by canon and accepted histories already established
Very simple explanation: The time-line was forked by the Borg invading earth in the past.
It was started post TNG era and was fought in the past. We don't really know who won it.
We do know that Archer was there for the final battle in the futuer but again we don't who won and what the out come of it was.
You know you're talking Star Trek, when a fork in the time-line is the "simple" explanation.
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That's so true.
I keep picturing the baffled look on Marty McFly's face when Doc Brown is trying to explain a forked time line and the creation of a parallel universe to him in Back to the Future, Part 2.