My view is that Starfleet has their "flagship" designs of a given era, of ships which are their best and newest tech in the most advanced hulls they can muster. These are the ships that everyone wants to see and serve on. Due to the expense of resources to build them, there would never be that many. The TOS Enterprise was one of a dozen like her, and I like to think that the initial batches of Excelsior, Ambassador, Galaxy and Sovereign class ships were treated the same way.
Some like the Excelsior would prove so successful (and easy enough to build in large numbers) that Starfleet would do just that, building dozens or hundreds of them while moving on to the next flagship design. So, we have a TON of Miranda class ships built as the workhorse of the late TOS and early 24th centuries; a large number of Excelsiors would be the next wave, and short of a huge war like the Dominion conflict to thin out those herds, lots of them would still be around to haul their butts back and forth between starbases.
And going back to the Ambassadors, well, in TOS the Enterprise was one of a dozen, but we saw MOST of them over the course of three years! While unlikely, it would be possible for the E-D to meet more than a few of her predecessors in seven years, especially given the more-than-average distances she travels (ref: Starship Mine).