To IAAL:
You will be happy to learn that the law is being revamped.
The actual intent of the original Florida "No-Fault" law was to reduce the amount of law suits for minor accidents. In the 1st test case for No-Fault the Fla. Supreme Court upheld the constitutionality of the tort exemption, saying in part:
"In exchange for the loss of a former right to recover (upon proving the other party to be at fault) for pain and suffering, etc., in cases where the thresholds of the statute are not met, the injured party is assured a speedy payment of his medical bills and compensation for lost income from his own insurer, even where the party was at fault. Additionally, he can recover for such expenses which are in excess of his policy limits by the traditional tort action, and may recover for tangible damage by means of such suit..."
The law has never quite worked because it was a compromise between "pure" no-fault and the traditional tort system. In the end the planitiff's bar found a way around the law and PIP suits became a huge money maker for lawyers. If the plaintiff wins a PIP suit against the insurer and the case was deemed difficult they can be awarded up to 3X their fees and cost.