darkwing_duck1
Vice Admiral
You know, my thought is this: there were probably so many Excelsiors and Mirandas built compared to how many Constitutions were built that there were still a decent number of them in service by the time the Dominion War was beginning, and a lot more in mothballs that could be quickly reactivated for service.
When you think about it, pretty much all of the other ships we saw in action (according to backstage materials) were at least in the NCC-5xxxx-ish range, which, to me, means they were probably built in the late 2340s or early 2350s. The only ones lower that I can think of were of those two classes - and those were only in the NCC-3xxxx range, with one or two possible exceptions.
Actually if you have the '99 Edition of the Encyclopedia (whose information all comes from either aired eps or backstage sources) the distribution is pretty even. Check out the list of starships with classes and registries.