I believe restriction on usage is different than a requirement to pay a fee to a non-government agency
but we know public entities all the time require Insurance, and last time I checked, Alstate/StaleFarm wasn't goverment either.... so you can get Alstate/StateFarm/AMA/Farmers/whoever to insure you as demanded by public control freaks.
The hard part is when they pick just 1 insurer to be acceptable, turning away folks that may have better coverage by another company just cause it wasnt StateFarm/AMA/"just the one approved insurer"