What if you put Jack Daniels in the fuel tank?
Some people believe ride-sharing has dramatically reduced DUIs in certain cities. Self driving cars despite the media hype and amplifying of every accident will be way safer than human drivers because human drivers text, drive distracted, drive sleepy, have medical conditions, or drive inebriated. So once self driving cars get good enough even their error rate won't compare to human beings rate of accidents.
Also once you don't have to drive the car it will be totally redesigned for both comfort and safety so even if there is an accident you'll be much more likely to survive. But this won't be for a while as people and lawmakers will still call for self driving cars where humans can still commandeer the system.
If a human makes a mistake and kills someone no one wants drastic action like banning all cars, but if an automated car did everyone would freak out and want them all banned right away.