No doubt the internal airlocks are there to serve as barriers between the various sections of the station. There would be the simple prudence of securing against catastrophic hull breach or spread of contaminants - a danger both due to the mining and refining functions, and because the station was there to intimidate Bajor and would face the wrath of Bajoran suicide bombers and possible other enemies of Cardassia. In addition, there would be the need to provide security barriers in contingencies: these airlocks were shown to feature weapons detectors and countermeasures ("Captive Pursuit") and would be effective in slowing down a rampaging boarding party or worker uprising. Finally, there would be a need for security barriers even in routine operations
, as we saw Bajoran workers frequent the Promenade area ("Necessary Evil") yet also work in the outer zones and travel by ships docking at the outer ring.
Quite possibly, such "airlocks" would exist at a great many locations inside the station for these three purposes; only the habitat ring, dedicated to trustworthy Cardassians, would have lots of regular doorways and few "airlocks".
Once the station became a trading hub under joint Bajoran/Starfleet control, the security arrangements would become a nuisance. But it would not be easy to rip them out. Also, just as you point out, there is no direct way to access the Promenade (say, an outer docking port or a transporter), yet the Promenade is the place everybody wants
to access, so retaining the security systems would be quite reasonable even for the new overlords.
Original set plans for the Promenade did include a multi-pad transporter, but it was never really constructed nor indicated to exist off screen. So other means of channeling the flow of people would have to be used, and hefty rolling gates sound just as good as any...
Incidentally, there are episodes where the station is indicated to harbor multiple vessels but the exterior shots show none docked ("Dax" is especially notorious). Perhaps this means that many vessels of smaller types actually dock at the habitat ring, in those bays also used by the runabouts, and for that reason are not visible even when present? This probably was a Cardassian practice already, considering the very existence of those bays. Passengers from such vessels would then be guided to walk to the Promenade along heavily secured routes featuring these rolling gates.