The all-inclusive dive resorts are a great place to get nitrox certified, as you have the evenings relatively free to study. We got certified so that the dive-fly times would be safer. Generally, cost of doing nitrox daily is somewhat prohibitive - at FI it was $10 extra per tank -the percentage was 32% and the fills were shorter, as mostly the DMs use them and they don't pump them up as much - cost at $10/tank- adds up at three dives per day - just not worth it to do daily...Don't think they limited bottom times at all, but the other tourists on the boat may get impatient if you're the only one down there for an additional 10 minutes on every dive. ..esp before LUNCH!! You won't bump into nitrogen limits or anywhere close - unless you do deep diving certification while there (on top of 3 daily dives) or do additional shore dives. Then, using Nitrox helps... Generally, the DMs bring you back to the boat area and you can play around there for the rest of your bottom time and practice your bubble rings or get more detail of the coral heads and the life in that area.
Oh, you DO have to have a NITROX card to get Nitrox there, but they don't "check you out" if you got the card.
BTW - with Nitrox, the bottom times aren't shorter - the max depth is shallower and the surface interval is shorter...