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 Perhaps Kirk's ship was the last of the Mohicans, a late example built as a casualty replacement and to the old and outdated specs for reasons of commonality.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