I hope driving on the road will not be banned, but instead hope for the more strict law for a driver's license. Too many people pay not enough attention to driving, some may check emails, some may lack ethics, some may roadrage with ridiculous reasons, and so on. We are lucky that those people do not love driving and therefore are likely to welcome the introduction of autonomous cars. There would be an autonomous-only license in the future, bad drivers eliminated first (and shifted to autonomous cars).
I also believe realistically an abrupt change as a total ban on driving would not happen, and instead there will be a more gradual shift to the driverless society, which would only materialize at the time I become too old to drive. I am completely fine with it, by that time I would have enjoyed plenty of driving.