Will they ever be the norm? Yes. Way sooner than anyone suspects. They will be so good that they will rapidly, rapidly accelerate as policymakers start to see their advantages. In more civilized, less fear and testosterone driven countries, they will be adopted rapidly and eventually we'll have to follow suit.
Far far faster than anyone is ready to admit now.
Except once there's enough cars out there, they will all be quietly talking to each other so they will know exactly what each other are going to do, and none of the cars will have the obnoxious egos that push people to show off, get aggressive, get pushy and drive dangerously.
In the end, no doubt, self-driving cars will be at fault in some collisions, but broadly speaking deaths from automobiles will drop precipitously, traffic will become more efficient and if adopted widely enough, the problem of parking will evaporate, opening up vast amounts of space for humans to live again.