Since several of them where in service before the NX-01...
And as everyone on this board has pointed out 100 times each, books aren't canon.
You're contradicting yourself here, because there's no actual canonical evidence that any
Intrepid-type ships were in service before NX-01, since the design never showed up onscreen until the second-season finale. So there's no proof that they were in service prior to 2153. As far as I can tell from Memory Beta, the basis for the claim that they were in service earlier is Eaglemoss's
Starships Collection magazine, which is no more canonical than the novels.
And of course the books aren't canonical, but they're contractually required to be
consistent with canon, so I based my extrapolations on the information that canon provided, which is my point. If there had been any canonical basis for positing that the
Intrepid type was older than the NX class, then of course I would've been obligated to go along with that, because that's what I'm paid to do. But in my judgment, the canonical evidence (specifically the ship's design, which is clearly derived from the NX class rather than the other way around) argued the opposite. And the fact that CBS Licensing didn't require me to change it is the proof that my interpretation is consistent with canon. Of course, they evidently approved Eaglemoss's interpretation too, but that just shows that the canon evidence is too sparse to resolve the issue either way. Which is why we have to look beyond facile appeals to authority and actually exercise our intelligence and judgment, e.g. by looking at the specifics of the designs and extrapolating which one is more likely derived from the other.