Solutions for this are pretty straightforward.
There is no need to mandate driverless cars, just remove any legal obstacles to having them on public roads.
Second, let insurance companies manage the rates for driverless cars vs. human-operated ones. It will probably turn out very quickly that it's much
less risky to insure a driverless car. Many people will switch just to save money on that side of it. If your insurance is going to be $200 a month if you drive the car yourself vs. $20 a month to have it self-drive, who's going to pass up that bargain? Most people won't.
Finally, require by a set date that all new vehicles sold come equipped with a self-driving system, the same way we've mandated airbags and anti-lock brakes.
Your insurance company can determine your discount based on how often you use the self-driving system rather than driving yourself. The more you drive yourself, the higher your rate will be.
Money talks, and a lot of people will decide that their desire to be "in control" is outweighed by saving money.