This doesn't mean that they are safe for adults, never mind children. I agree that these are often offered as a mode of transportation in the Caribbean; however, I have always been able to find a taxi or other vehicle with seatbelt.
This is the choice we make for our family, and I understand that others make different choices. That doesn't mean that there are "no seatbelt in Mexico" as is often cited on this (and other) forums. It comes down to how important is it to you to use seatbelts. It is very important to me and my family, so we find ways of making it work while still enjoying our vacation.
I hate hearing people say they don't bring a car seat because they were told that it was not an option, which is not true.