The Badger makes some good points. I'd like to add another one, just for the helluvit.
While Sisko's Defiant prototype proved to be an effective combat vessel to aid in the Federation's survival, the notion of mass-production of this class of ship raises unique security questions: The Defiant proved to have unusually good offensive capabilities, in addition to its defensive capacity. Even one of these ships, falling into the wrong hands, could prove to be an incredibly powerful weapon that could destabilize even major galactic powers.
Witness the third-year DS9 adventure "Defiant".
Given this, and given the thoughtful leadership of the Federation and Starfleet, one could easily surmise that the question of the Defiant-class warships' security simply had to come up. Even if there were some "security key" that could disable the ship's cloaking device and weapons (which Kira foollishly disabled when twin-Riker stole the ship), the Federation would have to consider the possibility that at least one of these warships would eventually fall into the wrong hands.
The Federation would also have to consider the possibility of large numbers of Defiant-class warships eventually being mothballed in the event that the Dominion invaders would be defeated and the war ended. What then? If large numbers of Defiant-class warships had been produced, Starfleet would wind up with a large number of
dunsels on its hands. So, what would the Federation do? Hollow-out an asteroid and store abandoned warships inside? Decommission most/all of these ships? (What if they were needed again to repel a Borg invasion?) And even if the Federation did mothball these little space-tanks inside "a great rock in space", Starfleet would have to protect and secure these crown jewels lest they be stolen or otherwise attacked while unmanned. To put it bluntly, would you want
Roger Korby to have a chance to infiltrate Starfleet and get his hands on one of these bluejays?
In some respects, the notion of the Defiant as a compact, uber-warship is "just what the doctor ordered" for security threats like the Dominion and the Borg. But the Defiant also signals the return to a
WAR GAMES scenario, or maybe
CRIMSON TIDE or
TWILIGHT'S LAST GLEAMING.
Given this, I think it's most likely that the Federation would maintain a small number of these warships, only producing an absolute minimum number to achieve military objectives. Beyond that, the security complications would quickly grow out of control.