I just don't like the idea of Starfleet laying down new keels on what was already declared to be an old and useless design in a previous movie.
From what we see, the Constitution
class indeed disappears right after the movie era. The appearance of a single example in "BoBW" doesn't mean the class would remain in service, as the anti-Borg flotilla seemed to feature quite a few "museum ships" or recycled study models from the pre-movie era. In-universe, we probably did see Starfleet Museum activate its orbital collection for a last-ditch defense...