Why would self-driving cars destroy the insurance industry?
Even if we ignore the ability of incumbents to fight bitter rearguard actions for years or decades when their economic interests are threatened; it's not as though self-driving actually changes the basic risks associated with cars. In an ideal world, automated cars may be more reliable than human drivers, certainly less likely to be drunk or exhausted; but unless they somehow achieve infallibility, there will still be periodic accidents. And the whole point of car insurance(and the fact that it is generally mandatory) is that a car accident can easily cause more damage than most operators can afford to pay for, especially if injuries or deaths stack up in addition to mechanical damage.
Nothing about the self-driving-ness changes any of this. It might change the determination of who is at fault; or increase the number of 'no culpability can be assigned' situations; but it will still be a situation of occasional ruinously expensive incidents with long periods of quiet, which is more or less exactly what insurance is constructed to cover.
There will, presumably, be lots of fun arguing over who exactly carries the insurance, and what sorts of failure modes become the vendor's problem vs. the 'known risks' that the operator takes in using an automated vehicle on the road; but the same basic factors are in play.
What will probably change is the flavor of actuarial data-mining that is popular: currently, it's all about scrutinizing the driver for direct and indirect signs of riskiness. If the driver isn't driving, they'll presumably shift to exhaustive scrutiny of system maintenance and where/when the vehicle is operated(since some roads and times of day will just be more risky than others). Insurers mapping out 'high-risk' zones and charging people who travel in them more definitely won't go badly or upset anyone. Not at all.