I don't think that is necessarily true.. The cost of insurance is based on the average expected payout per customer... I don't think the average payout will increase, as being a human driver won't suddenly become MORE dangerous, at worst it will stay the same.
But what happens when the average expected payout is expected to go down? Insurance companies will expect lower loss ratios from self-driven cars, so doing something as dangerous as driving your own vehicle will carry a premium. Its very similar to how your health insurance premiums are much higher if you're a smoker. You can smoke, but you're going to be charged for this unnecessary, harmful action.
Oh, I have no doubt that driving your own car will be more expensive than taking a self-driving car. My point was that it wouldn't be more expensive than it currently is to have insurance (when everyone is driving their own car)
