You are assuming that the government will run the insurance process competently. The government already is beholden to the voters and public opinion and they are just so efficient and devoid of red tape right? You're also assuming the government will run the insurance industry as some sort of benevolent not for profit as opposed to a new form of tax. Not to mention what happens when the republicans get in and decide to raise insurance on electric vehicles or manipulate the price of insurance on cars from certain countries as a form of ersatz import tariff, or install political appointment figureheads who can take kickbacks to make certain manufacturers cheaper to insure. Not to mention the formation of a government department of adjusters and estimators to run the whole deal.

The existing system sucks buy I dont see the government having total control and no alternatives being some sort of magical panacea.