I would try to argue that no one thought the audience would be confusing the ship on screen with a "hero" ship when they showed all kinds of Galaxy class ships on DS9, but then considering how often I heard people say "is that the Enterprise?"...
One must also consider the first time DS9 showed a Galaxy class, it was to blow it up to make a point. Afterward, all the ones we saw were after the Enterprise-D was (grumble) destroyed and it was technically no longer a Hero Ship. TNG had overlap with the TOS movies, which is probably why they avoided showing operational Constitution class ships - even though it was 80 years later, they were still making the movies with them in them. Which in turn probably explains why there was never a CGI model made of it, which is why we didn't see them in action on DS9 or VGR.
To further confuse my earlier point, in TOS, whenever they showed another starship, it was almost always another Connie.
It's obvious. Someone clearly ordered 30 Reliant class ships to take light duties away from the larger more adaptable vessels. Someone mistook a smiley face for a zero and they ended up with 300. So now they're just trying to wear the damn things out!
And really, that's the only reason why Starfleet keeps going to war. The Dominion? C'mon now, the war wouldn't have happened if the Federation didn't keep butting into sovereign territory Consequently, what ship is most often seen on the front lines? That's right, the Miranda. And some of them *still* survived the war. Boo-yah!
I think the main reason why Miranda's were abundant in the Dominion war was due to how the series creators wanted to make the battles scenes. The Dominion had big ships and little ships which are faster and since the Defiant is considered a prototype, I think they chose the Miranda to be the Starfleet equivalent to the Klingon Bird of Prey or The Dominion fighters. That way you have this nice effect of little ships weaving in between the big ships. I really think that was the only reason they were so common and the registries suggest a fair amount of them were built some time in the early 24th century making them not too old.
Holy four-year-old thread revive, Batman! And no, the reason why Mirandas were in the DS9 fleet scenes was because ILM made a Miranda CGI model for FC which along with the Akira, SAber and Steamrunner, were given to CBS for use in DS9. It had nothing to do with how big or small the ships were.
Star Fleets use of Miranda Class ships in the Dominion War reminds me too much of "Operation Human Shield" from South Park: Bigger Longer & Uncut.