I have gone to Cozumel as a single diver many times. Often, the plan was cheap lodging downtown, and spend my money on diving and eating, although I was only rarely going for more than two dives a day. I found that with very long bottom times (Aldora has HP Steel 120 tanks), averaging over an hour - even 90 minutes - per dive, that was enough for me, usually with a night dive thrown in during the week.
A couple of things to think about in planning a trip to Cozumel. First, the shore diving is not that great; the good reefs are all offshore and boat diving is the attraction. Most operators offer 2-tank morning dive trips. There ARE operations that offer afternoon 1-tank trips - Aldora just started offering afternoon dives from its Villa, north of downtown, and Dive Paradise, the house op at Hotel Cozumel, also will do afternoon trips. Most Ops will offer night dives IF there are enough people interested; it can be a chore trying to organize 5 or 6 folks all willing to do a night dive on the same night (although it's probably easier if you are staying at a dedicated dive resort, like Scuba Club Cozumel, Blue Angel, or the Aldora Villas).
One BIG attraction of Cozumel, at least for me, is the wide variety of very good to excellent restaurants, with a variety of cuisines and in every price range. That is why I willingly never do All Inclusives in Cozumel. The only time I did was at Hotel Cozumel for a Scuba Board Invasion; I liked the Hotel, and it was a good location, an easy 15 minute walk to town for lunches and dinners, but the food was, in my opinion (and I set the bar high, I am a foodie) TERRIBLE. Breakfast was OK, although the coffee was little more than dirty dishwater, but Lunches and Dinners were tasteless, bland, and occasionally inedible. I would gladly stay at Hotel Cozumel again, but I would NOT opt for the AI plan. The only exception might be if you are a heavy drinker and were planning on drinking your money's worth at the bar, while still going out for meals, but diving 4 times a day would significantly cut into your drinking time, I would assume, and I can't speak for you, but I don't enjoy diving on a hangover.
There are a LOT of good Dive Ops on Cozumel, from the high end valet service ops like Aldora, Blue XTC, Liquid Blue, Tres Pelicanos, etc., to the more bargain friendly, but still very good ops like Dive with Martin. My personal preference is Aldora, I like the Steel tanks (more air AND better buoyancy characteristics), long bottom times, long SI at a beach club, excellent DMs, and they take care of all your equipment (except wet suits; not important to me, a sore point with others), but I have also dove many times with Dive with Martin, and don't have any complaints (well, except for one time; I arranged for AL 100 tanks, and when I got my tank for the second dive, the valve had been left slightly open on the boat, so I only had 2100 psi before I even went in - so much for more air in a bigger tank). Figure out just what you want in a Dive Op, and you can find one that will meet your needs. I've never used them before, but I understand that Liquid Blue offers both a 2-tank AM dive and a 2-tank Twilight dive, so that might fit your desire for 4 dives a day. I have no idea if that's an everyday thing or only when there are enough takers.