The reality is that DM-led dives in places like Cozumel are going to be reasonably safe with or without a computer as long as you use a little bit of common sense. Common sense mostly means staying about the same depth or shallower than the DM.
If you think about it, the DMs not only want to keep the divers safe, they have to learn to tailor their profiles so that none of the common computers go into deco. The normal deep Coz dive, for example, will only have a few minutes at the deepest part and then a leisurely ascent to somewhere in the 60-70' range for many minutes and then another bunch of time around 30'. Second dives are almost always shallow as are afternoon and night dives. Even outfits like Aldora, which prides itself on the length of its dives, will have a lot of that extra time spent drifting along at the nitrogen loading equivalent of safety stop depth given their high 02 level nitrox mixes.
Even wreck dives in vacation spots are as SurfGF friendly as possible with the DM usually doing a quick lap or half lap at the bottom before moving up to the highest points on the wreck. I'm also convinced that they often they push the speed a bit or expose the group to more current than necessary during the deep part to "help" divers run out of gas before they run out of NDL time.