They charge insurance companies because it is a commercial operator  

Suppose AMC sent you a bill in the mail for $5.00 out of the blue and told you if you don't pay it, they will put a lien on your home and seek to forclose it due to not paying??

Miami Dade does not bill insurance companies and were told by the FAA they cannot!   Lee County's program was shut down because it was billing insurance companies.   They operated public aircraft as well.

There is a HUGE economical advantage to being a government entity operating public aircraft (bought and paid for by tax payers) and also being a commercial operator in direct competition with other certificate holders, be it non-profits or for-profits.   They are a government operator collecting tax revenues to cover their costs.  They should not ALSO collect insurance money as a source of revenue, period!  They are double dipping!