Should a person carry uninsured car coverage even in a no-fault state like Florida?

If a person possesses a normal health insurance that covers the injuries occurring in an accident, it might lead to the thinking that uninsured car coverage would not be necessary, because it would cover only bodily injury and not the damage to the vehicle. However, in Florida, a PIP is required, which would be usually a minimum of $10,000. Hence, that person could end up with three policies of health policy, uninsured car coverage, and PIP. Further, health policies pay only limited amounts and it would not cover the costs of a nurse taking care of an injured family member. Moreover, the uninsured car cover would compensate the lost wages and include the benefit for pain and suffering but the health insurance would not.