Pretty sure this has to do with lack of awareness. Yes, Negril.com has definitely helped with the awareness, but how many visitors to Jamaica do not use this site? IMO, there needs to be a media campaign, maybe starting with JUTA and the tourism authority to help bring about awareness, maybe even using posters in the airport.
Some of these illegal taxis are highly rated on TripAdvisor! Yeah it may be a lot more work for them, but perhaps TripAdvisor should not allow ratings unless you're licensed and legally allowed to perform the service for which you are being rated on? I could see some sue happy people suing TripAdvisor, "well he was highly rated on your site."
Just my .02.
~Moose