Insurance and liability become a lot simpler if you just don't touch the controls at all. There will be a clear split between people who don't drive and therefore are not liable and the remaining group that still drives and is causing most of the remaining accidents (and cost for insurers). That's going to inevitably get more scrutiny from everybody: insurers, authorities, occupants of self driving vehicles, other manual drivers.

This will probably be insurance driven. If you don't need to drive anymore, you don't actually need a license. And if you are not driving, you can't be held liable for damage caused by your vehicle. You'll still need insurance to cover any damage/harm your vehicle might cause but this will likely be quite cheap given autonomous cars are safer and on average don't really get involved in accidents. It's quite possible that eventually just gets folded into warranty terms for your car and covered by the manufacturer.

As manually driving increasingly becomes a choice rather than a necessity, your insurance for that might become conditional on you being current and proficient in the same sense that licensed pilots need to regularly do check rides to verify they can still safely operate a plane. Additionally, insurers might insist on you passing a regular health checks to verify that you are still fit enough to drive. Some countries already test elderly drivers but there are lots of elderly people with pretty serious health issues passing these tests as well. Expect this to get a lot more strict.

just to illustrate the idea, not saying these are the exact numbers:

1. $1000 a month to drive yourself and still risk liability

2. $50 a month to have the car drive you, and GOOGL takes excess liability