It's been understanding that the detailed paneled surface of the ship itself was meant to represent the ablative armor. This is why we don't see some of the traditional details we're used to seeing on other ships, like standard segmented hull lines representing the presence of a deflector shield grid. Even things that got identified later on, such as thrusters, torpedo launchers, and transporter emitters, don't appear to be the same common variety in use by the rest of Starfleet. They're all covered with armor.
As for why the hull never appeared to be burning or breaking away as the armor was damage, as the name suggests, I would imagine it has to do with the limits of CGI budgets. Consider that quite often many ships didn't even appear to have shields because it would have been cost/labor intensive for the large fleet scenes, as you can guess at what it might have taken for them to show consistent damage throughout a battle.
Not to cross forums, but consistent damage has long been a sticking point against Voyager, though they certainly tried to make up for it with the USS Equinox. Outside of Trek, only one recent show that I know of has done a good job with showing consistent and accumulative damage, and that's BSG. It certainly added a great deal of realism to the show, to see the Galactica actually taking damage, some of which couldn't be repaired, leaving her hull scared and burned.
Timo brought up an inserting point I hadn't thought of, a few posts above, in regards to what the Defiant was up to, during the battle against the Klingons in Way of the Warrior. The ship had taken some damage during the mission to rescue Dukat, but it hardly seemed to slow them down at all.
I wonder why Sisko didn't leave Dax or Kira on board in command of a skeleton crew, and give them orders to engage the Klingons, particularly given the number of times Defiant was off doing something while action was happening on the station later on. So it's not like they had anything against splitting up the action. It seems strange now, that for the entire battle, we didn't see the Defiant at all and while the ship is certainly tough, I doubt it would have lasted long given the amount of weapons fire that was being exchanged.
If not in the fight, then surely Sisko would have ordered a skeleton crew to take the ship to Bajor and wait for Starfleet reinforcements.
Perhaps adding those elements would have disrupted the flow of the episode...or pushed it over in time.