The 'real' reason is this:
If you want (what I think) is the real reason: TPTB probably felt that since the Constitution Class Enterprise was a "hero" ship, there can't be another ship on screen that looked like it, since it could cause some confusion among the audience.
But that's just my two cents worth.
It's the same reason we saw no
Sovereign class or
Intrepid class ships n the Dominion War. (And yes, I'm aware of the
Bellerophon. I'm pretty sure that was an economic reuse of the VGR sets and was clearly the single exception.)
My explanation was that in the late 23rd century, Starfleet built thousands of Miranda and Excelsior class ships, then put most into storage in case they needed them again.
Now they pull them out of storage and put them into action as needed. Like when the Dominion destroys large numbers of vessels during the war.
That would explain why the Federation seems to so easily overcome staggering combat losses in relatively short order.
I've had to do a lot of thinking about this in trying to reconcile all of this for the purposes of my Excelsior Tech Manual (see
here.) While I haven't gone into the
Miranda much yet (and won't much at all) it has factored into my thinking. I'd say it's only partly that they were built in high numbers. I personally believe that the design was part of it;
Miranda was 'only' launched in the late 2250s, making it slightly newer. I also believe that its design is intrinsically more adaptable and useful for a wider variety of missions than the
Constitution - as we've seen it in missions from cargo transport to scientific on TNG alone.
I think the treaty with the Klingons post TUC had limits on the numbers and types of ships that the Federation could operate, and that Starfleet phased out almost all of the older
Constitution class in favor of the newer
Excelsiors that were designed to replace them because they were ships of the line and points of contention with the Klingons. Several decommissioned
Constitutions would then be placed in reserve fleets, while a few might not be decommissioned at all.
Mirandas, on the other hand, were 'only' frigates and were presumably exempt from the same limitations, as they could be written off as 'research ships' or 'transports' while still packing a wallop. Likewise, it might have proven more economical to keep the
Miranda rather than develop a totally new design, especially if they could make use of parts from the retired
Constitution class ships for repairs to extend their lifespan. (I postulate later in the ExcelsiorTM that the
Centaur was an example of an
Excelsior-contemporary designed to replace the
Miranda which ultimately did not prove itself as an improvement over the
Miranda.)
For what it's worth, we saw wreckage of a
Constitution class ship in 'Best of Both Worlds Part II' in the Battle of Wolf 359, the same footage again in 'Unification' in the Qualor II Surplus Yard (perhaps the same ship, perhaps not) and again in DS9's 'The Sound of Her Voice' as the wreckage of the
U.S.S. Olympia. All of these instances were reuses of the 'destroyed'
Enterprise from TSFS. So they're still around to some extent. There just aren't many, or enough for us to see them very often.
