I think there will still be requirements for a license but it will be about the state apparatus' interest in controlling movement of citizens and not about driving the car.
At first, it will still be about "driving" as I think that the transition to self-driving cars will be somewhat gradual. I don't think it will be the case that this year's model is manual and next year's is fully automated. Automation will be phased in where the car can handle more and more routine driving situations until eventually no driver control will be required, and during this transition it will still be possible (and necessary) to actually drive the car.
Even the first fully automated cars will probably allow some kind of user overrides as to where the car goes, how fast, etc, so you will still need to have a driver responsible.
But after cars become fully automated, it won't be about "driving" anymore, it will be about the state's interest in controlling who can go where and when.