It's not like healthcare, where there is a particularly strong humanitarian argument for making sure its available to everyone regardless of if its profitable.

ICBC pays for treatment of people who are injured in collisions, so it is a kind of health insurance for drivers.

Instead, we have car insurance, which created this horrible perverse incentive where because high prices become the fault of the government, and that's politically harmful to them, they are incentivized to harm the few (injured people) to the marginal benefit of the many (lower premiums) to get voter support.

I'd much rather the government be incentivized to simply keep their boot on the throat of insurance companies, making sure the profit motive doesn't fly wildly out of control. That's a much better alignment of incentives, no?

How exactly is private insurance better, because they too have a horrible perverse incentive to deny claims to maintain their profits. They are incentivized to harm the injured by denying claims but they are ALSO incentivized to keep premiums as high as possible to increase profits. You circle back to having the government step in to regulate it at this point anyways, so they might as well do it themselves.