People are going to give up their steering wheels kicking and screaming but the roads, particularly in urban and metropolitan areas, would be safer if we all used robot cars.
Humans, as a species, can't drive for shit. Too selfish, too self-absorbed, and too aggressive. The last 20+ years or so of obscene traffic in our major cities has basically provided all the evidence we will ever need to factually state that robot cars would save lives.
Unfortunately humans, as a species, have another detrimental characteristic. We don't actually place much value on facts that don't either maintain our comfortable status quo or benefit us directly and immediately.
The robot car is the invention that could save thousands of lives annually but we will be so slow to adopt them that I suspect it will be decades before the mainstream population accepts them.
Folks in rural areas are a different thing. I can understand why Bubba Joe in a town of 1000 people in western Montana doesn't have a use for the tech and doesn't want anything to do with it. The lack of traffic, the amount of dirt roads..etc etc...that makes sense to me.