Good riddance to an entire industry
Seems to me that the death knell of the auto insurance industry has started to toll. It'll take time, to be sure, but when you factor in—
* Robo-cars will have orders of magnitude fewer accidents than those driven by people, 50% of whom become idiots as soon as they're behind the wheel. The remaining accidents will rarely lead to expensive claims because of lower speeds.
* Insurers will cease to insure individuals because the latter have turned into passengers and there is very little for actuaries to do: some people being born now won't ever have a "driving record".
* Soon enough the risk and consequential damage disparity between human- and robo-driven cars will force most drivers off the road either by law or through prohibitive premiums. There will also be a cultural sea-change, to the point where the majority of people will prefer *not* to ride in a human-controlled vehicle.
* The premium-hiking manipulations of insurers will cease, for the above reasons and because your premium won't be doubled because you got nicked once two years ago for speeding, or failed a drug test, or ran a red light (whose enforcement cameras, in some jurisdictions, are actually paid for by insurance companies to increase offence rates so that premiums can be raised). Or because you've had your 55th birthday and had a no-fault accident, leading to a tripled premium next year.
* The highly lucrative area of disputed claims will largely vanish, as black boxes and cameras will tell all. Insurers *and* their ambulance-chasing parasites known as lawyers will stop cashing in.
—it's hard to see much point in having hundreds of insurance companies all pitching their "unique" and "special" products (which are designed with bells, whistles and mostly valueless "extras" to make it impossible to compare like for like on price), none of whom will make significant profits any more.
By which point the government might as well create a national transport insurance agency, integrate it completely with vehicle licensing and taxation, and put any surpluses back into the Treasury.
As arguably the only industry even more corrupt and dishonest than banking, it will be a case of good riddance to auto insurance.