Just an idea...
What if, instead of requiring by law that people pay for car insurance. They required by law that you pay into a bank account in the same way? Similar to social security or medicare kind of.
Then you would be invested and incentivize more not to get into a car accident if you could get that money back in retirement or in case of a disability where you can't drive or give up your drivers license. The more money you get into your account, the less you should have to pay each month. It's a mandatory saving account in case of accident.
If you get in an accident, then it pulls money out of your account.
Paying into an insurance company you are paying labor for all the people who work for that insurance company so there might be less jobs, but on the other hand those jobs could be replaced by people managing the bank account system and calculating how much a person should be paying into it.