Back in the late 1970s, into the 1980s, when Cozumel's charms started to be better known as a good place to vacation (especially for divers), there were only old, funky cars that were considered a part of the ambiance. The cars on the retail market would tend to rust out and get ragged after a few years as something about the salt air was far more corrosive than any beach location I have seen (many). Renting a bug or a "VW Thing" were your only options. No matter that the brakes might not be great, it was still a small town (20,000 population), minimal traffic, a safe and friendly place to drive.
Now their are a group of people dedicated to having adventures behind the wheel. I like driving to adventures, but I prefer no excitement, nor adventure from the simple act of driving the car and hoping it makes it to and from destination without incidents. Some wouldn't want a car that you couldn't see the pavement through the floor boards
Two local companies, LessPay and Isis rent a number of more well used cars. They are maintained and attention paid to keeping them on the road. I know LessPay and I assume Isis have their own mechanics on salary who can fix mechanical problems and repair any body damage cheaply. A dented fender might be $30 dollars, not a $500 dollar new replacement which doesn't exist.
LessPay insurance will cover all damages, provided you do have the insurance included as usual. All rentals are required to include liability. What I find amusing are the constant posts on TA praising Isis and ALL insurance included. As a joke I have tested how many posts I can make and have deleted because I mention the 10% deductible of Isis. It is significantly cheaper to have 10% deductible insurance and Margarita is not one to take advantage. I'd be more reluctant to have 10% deductible with some of the common U.S. brand name companies, which have zero in common with the north of the border except to use their reservation system to get great deals on rentals, $75 to $110 a week. Those online reservations cause complaints when people discover that with the needed insurance, add a couple hundred to those "cheep" rates.
When doing rentals, it's not a bad idea to take a good look at tires. I did have a major tire problem once that had escaped my detection as well as a tire shop. I'd check brakes and tail lights. Wise to check windshield wipers too. Dealing with the actual local companies, I'd just eye ball the body as the plus of dealing with the "well used" a little dent or scratch just doesn't matter. I don't like parking new cars in busy parking lots as they always get scratched from other's car doors..