Someone will have to sell insurance to car manufacturers for the remaining 10 percent of accidents.

I don't think that's necessarily true - insurance companies make money out of insuring far safer modes of transport than driving (like air travel). The liability merely shifts from the driver to the software developer. Whoever is providing the self-driving cars will need to have large amounts of indemnity insurance to cover potential losses.

The second part might be true, but human-driven cars are going to be on the road for a very long time. As long as they are here, accidents will happen, and insurance companies will find a way to charge you for it. Geico et al will never stop existing, so long as there is the possibility of human error.

People will still want and demand car insurance. Stuff still happens, and I want my car and injuries paid for. So they'll still be around. It may be a smaller industry, but it won't kill them.