Yes they were old ships by that point but the Oberth, Miranda and Excelsior classes were still in service so why not the constitution class? They more than proved how capable they are during the 5 year mission runs.
Classic rationalizations: 1) Perhaps Constitutions were much older than any of the other classes; them being refitted into tech standards that the Mirandas and Oberths represented from the onset did not appreciably prolong their service lives. 2) Perhaps Constitutions were the silver bullet application of the Miranda tech, built in very low numbers compared to the more utilitarian design; simple statistics would then dictate us seeing so many more of the latter, even if a scant few of the former did survive till Picard's days. 3) Perhaps Constitutions always were complete duds, with Kirk the only one able to achieve anything substantial with those. #1 might be supported by the lowest Constitution registries being in the 1000 range while the lowest Mirandas are in the 1800 range. Perhaps Kirk's ship was the last of the Mohicans, a late example built as a casualty replacement and to the old and outdated specs for reasons of commonality. Then again, the lowest Oberth registries are even lower - but that ship is a science type, unlikely to participate in any sort of a rat race. If the Oberth sufficed for surveying green supergiants and studying sapient algae in the 2210s, then it would suffice for that in the 2530s still, as such "threats" would not evolve. #2 might gain support simply from direct observation. We only ever see two Constitutions of the refitted configuration, assorted partial sightings (mere nacelles or secondary hulls) notwithstanding. Mirandas in turn are indeed everywhere. And the relationship between Galaxy and Nebula seems similar, even if the former make a few more appearances in the Dominion War relatively speaking. #3 always was an option until the latest show, but now DSC seems to be saying that Constitutions are hot for the 2250s, even in comparison with much larger and more modern-looking types on the forefront. Beyond those, there's always the possibility that a special mission sees one type or the other predominantly deployed off camera. But Kirk's ship seemed to be as generic as ships get, always being assigned the most diverse menial tasks instead of being held in reserve for special duty X. And TNG in turn seems to make Miranda the generic party. Timo Saloniemi
The model was a nightmare to use. And they probably wanted to keep it "special" for TOS movies, which were an ongoing thing when TNG began. FWIW, the Stargazer was originally Constitution-class, but changed in post-production when they decided to build a new model.
I've always favoured the idea that with the Mirandas covering the "fleet workhorse" position and the Excelsiors as the new "top-of-the-line"."trailblazer" that the Connies weren't the priority and that they largely fell by the wayside as the decades went by. I've also seen it suggested that the Kitomer Accords may have had (in-)direct force reduction implications and Starfleet Command opted to sacrifice the aging Connies (and some or most of the other 2230s-2250s designs like Walker and Shepard classes) to preserve slots for the newer Mirandas, Excelsiors and later the Constellations and Centaur-types.
I must admit that I prefer the sphere at the front of the Starship as they created for the Star Trek Encyclopedia's back in the nineties than the flat mushroom versions as seen in ENT! JB
There was a Constitution saucer and secondary hull in the wreckage of the battle of Wolf 359 (a reuse of the destroyed Enterprise model from STIII). It's possible that since they were seen separately they were just components of other ship classes, but it's also possible that it was an intact Connie that had its saucer ripped off during the battle. The STIII Enterprise saucer was also used again to represent the wreckage of the U.S.S. Olympia in DS9, so that's another possible instance of a Connie operating during the TNG era. There's also a mention in DS9 about the U.S.S. Republic being used as a cadet training vessel. I believe the writers mentioned that the ship was supposed to be the original Connie that Kirk served on.
I admit, I've always found it weird that the Trek production staff seemed reluctant to use a design in multiple series (even if only occasionally) for fear that it would "confuse" viewers. Hence why we rarely saw Intrepids outside of VOY, with the occasional exception. For my head canon, I tend to think the refit heavy cruisers continued to stay in service along with other contemporaries like the Miranda, but I agree with the suggestion by Jackill and other sources that the Excelsiors eventually began to fill this role after the design was no longer a battleship (FASA's intended designation). FASA suggested that at the time of the Four Years War in TOS, Starfleet avoided using original Connies on the front lines because they were considered highly advanced for the time, and Starfleet didn't want to risk capture by Klingon forces.
I just go with the idea that just because we didn't see them doesn't mean they weren't there, rather than trying to think of all the reasons why ships that happened to have CG models available during DS9 were overrepresented compared to the Norways, Ambassadors, Oberths, Novas, all the BoBW ships, Constellations, and, yes, Constitutions.
Maybe there weren't that many of them to begin with. Kirk's line in TOS about Enterprise that there were "Twelve like her in the fleet" seems to hint this direction. Also, there seemed to be a pretty high rate of Constitution class ships getting broken or otherwise blowed-up (Intrepid, Defiant, Constellation and a couple others I can't think of off the top of my head). Going with these two thoughts, my conclusion is that there just weren't any more Constitution class ships left by the middle of the 24th century. Your mileage may vary.
I meant more in universe reasons that the real reasons like they thought we were so dumb that we would see a Connie and think it was original Enterprise (how insulting).
Well, most writing staff wants to target the lowest common denominator of audience which is bad enough in itself.
Back then there would have been an image problem because the refit is THE Enterprise, the D didn't have so much history to it yet so yeah, confusion, the model was indeed large, heavy and also not in a super shape during/after the movies were done, battle damage had been added, it also was repainted at some stage etc etc. In universe, they're long range explorers, they simply might be far away and since there weren't too many of them that would make them rare so to say.
But they do use dilithium and antimatter. More efficient engines means you can build two ships for the material usage of one. Or build a larger ship that uses the same about of fuel/materials. This would be cost in materials rather than money. And Starfleet was always looking for more dilithium in the 23rd century. And still seem to look for it from time to time in the 24th century. Their big concern seems to be deuterium (for silly reasons given how common that stuff should be).
In the movies, it seems that the Constitution is being retired in favor of the Miranda which is smaller and the Excelsior which is bigger. If this is meant to upset the audience, it works However, this may be like the real navy, in which, as I understand it, mostly carriers and destroyers are used, because either the biggest and most powerful ship is needed for a major show of strength display, or else the destroyers and their missiles are big enough. This may parallel what Star Fleet was planning to due, phasing out medium-sized vessels. Regarding the registries, perhaps some numbers were set aside. Maybe destroyers and Scouts start at 500, making the Oberth's numbers like 638, actually making it a newer Scout, then the Cruisers don't start until 1000 or 1500.