Most highway codes are written in such a way that the driver is liable for any damages, and by implication the driver has to be a person. Liability is regardless of who pays the actual bill, so for uninsured drivers there is still a liability that rest with the driver. The insurance company is not liable, so the insurance company paying for damages that you as a driver is liable for, does not change liability.
What needneeds to change is simply the highway codes, so that the owner of the car can be liable rather than the driver of the car. OnceOnce the owner of the car is liable, a driver lessdriverless car can be insured through the fact that the owner can take out a liability insurance that would cover regardless of who is traveling in the driverless car.