Hi, Colin!
We did a lot of research on this about a year ago. From an informal poll of about 8 or so other newer complexes, about half had the public liability and half did not. One of them had a claim (which I think was not paid b/c the person hurt was intoxicated), but the rest had no claims and no problems. For those that did not, they had the same reasoning as you state above - liability claims would not be heard; if it was heard, it would take years to be resolved (and most visitors would not have the patience/money/time to wait on the Belize court system), etc. There was even a statement that Belize law does not even define liability, as it is more "you are responsible for yourself" culture. I can't support or refute this claim, though, as I have limited knowledge of Belize law.
I think you would receive a "yes, you definitely need insurance" response if you checked w/ an insurance company about the need for insurance...