In some of the reading I've done about self-driving cars it seems that they are overall much safer and far more reliable than humans. There is the idea that these cars will lose control or be hacked and kill people, which could happen, but those things would probably be pretty rare. The cars would NOT, however, be drunk, or fall asleep, or text, or follow too close, or put on makeup, or get into high-speed chases, or race, or read, or have sex, or do any of the other things that humans do when driving which kill and maim so many people.
We always tend to be afraid of new technology, and then can't imagine living without it. I remember reading that when the automobile was first being introduced people were up in arms about the noise, the speed, the danger, the fact that it frightened the horses, and so on. In pretty much every other area of our life we welcome technological breakthroughs, and this should be no exception. In fact, it's the next logical step from where modern cars already are.