Don't know about the US but in Australia it's the car that is insured (for damage suffered by occupants, third parties and third party property as well as to the vehicle of course, as well as for theft), and not the individual. Indeed 3rd party insurance is compulsory here in order to register a vehicle.
I don't know Australian law, but I would be surprised if it works the way you describe for liability coverage. Cars can't have liability, their owners and operators can. It's the owner/operator who is therefore insured. In the US there are several different types of insurance available, all of them usually wrapped into a single policy:
Liability: Covers the operator's liability if s/he causes an accident. Pays for property damage and personal injury. Regular operators must be listed on the policy and rating us based on their driving history, age, gender, etc. Failure to list a regular operator could result in denial of coverage if that operator causes an accident. Infrequent operators will be covered if they do not live with the owner.
Collision: Covers damages to your vehicle in accidents caused by covered operators.
Comprehensive: Covers non-collision damage to or loss of covered vehicles (tree limb, fire, theft, etc.).
Medical Payments: Covers medical expenses for injuries sustained by covered operator and his passengers on a no-fault basis.
Uninsured/Underinsured Motorist: Covers your injuries, property damage, etc., caused by an uninsured or underinsured motorist. It essentially insures you against the the uncovered liabilities of others.Phooey:
I still don't understand why you think this is going to require a major change in the way insurance is done. Companies are already
insuring vehicles which can drive substantially on their own, which can stop or take evasive action on their own in emergencies, and which can park on their own. Why would a fully autonomous vehicle be covered any differently?