Well maybe you would change your opinion if private firefighters would arrive to your burning house and told you that they will buy it for 50 EUR, or they will let it burn to the ground. You will lose your hose in both cases.
I think you need to sign a contract with the firefighters before shit starts burning. Car insurance, health insurance, any similar market driven service would not let you insure AFTER the accident either.
I actually described how it was done in ancient Rome under Crassus