I think a lot of the "real life" reason for the Miranda's in bulk on DS9 and TNG in general was the nature of the battle the writers wanted to portray. The Dominion had really big ships, middle sized ships and little fighter type ships. So you start to see a tiered dogfight kinda effect, the big slow ships lurking and the little quick ships darting in between. I think they wanted a Federation equivalent to the Klingon Bird of Prey or Jam Hadar fighter and since the Defiant was supposed to be a "new class" the only available small ship saved in CGI format was the Miranda class. I know people are critical of their presence in such an intense battle but to be fair I thought they fit in nicely and I'd rather be in one of those than an Excelsior class. Yeah the Miranda bought it easy but only if they were caught while the midsized midpaced excelsior and akira classes were looking like swiss cheese through most of the battle scenes.
As to why the Constitution class was not used in TNG it just sounds to me that someone (maybe Rick Berman) made a decision that the ship design would not be utilized due to its familiarity with the original crew (sounds fishy to me) and the in universe explanation was that it was an outdated design. While I don't find any real rationale to support this I did hear once that the model of the refit connie was a big heavy pain to film and possibly was in a different studio?
Regarding "in universe" it does seem that the only ships by the 2370's to be active were ships with 5 number registries. And with the exception of a few lumbering stalwarts (The Repulse, Victory, Trial, and The Republic) the vast majority of 4 digit registry ships were retired or mothballed (like the Constellation class) sometime prior to the start of TNG. I do know that someone (maybe Okuda) wanted all TNG era ships to have 5 numbers and I think the general idea was that those first ncc-500-10,000 ships were built in the 23rd and very early 24th century making them all pretty old by the Dominion wars. Since it seems that the Constitution class run ended somewhere in the 2000's and the Miranda's up to 30,000 they were old but not quite as archaic as the connie. That said it does bring up the odd question how so many more ships were built in only 70-80 years time. I mean 10,000-80,000 in just under 70 years?? That's like 7 times the ships of the prior century and means about 3 ships built every day lol