The moment you start mass-producing self-driving cars, people will start dying in accidents that were caused by them. Even if they are vastly safer than human drivers^+ , the sheer amount of cars on the highway and the varied situations they get in will mean that there will be accidents caused directly by bad decisions done by the computer. The legal system we have is a lot more lenient to human error than it is to other causes, and this is a major problem, because it means that even if going all AI cars would mean that we lower the fatality rate by 97%, that still means a thousand deaths a year that can be blamed on one company. That company could not possibly continue operating, even if they would be saving 29000 lives every year.

I am generally not a fan of the Chinese government, but this is one way in which their system is better than ours. They have people in positions where they can do the math and decide that if some decision greatly saves lives on the net, they can enact it even if it directly causes (less) lives to be lost.

^+ And really, that isn't a hard goal to reach. People largely don't cause fatalities because they are bad at driving, they cause them because they are impaired in one way or another and because the reaction times at high speeds are too hard for humans. Most early AI cars will probably be shitty, but they will largely be shitty in ways that don't endanger the occupants.