Insurers don't care all that much if you rear end someone or get in some other "normal" accident. That happens enough that they have figured out how to cover the cost at scale. They don't take that much of a hit anyway because of your increased premium over time. They'd obviously prefer you do it less but so long as their slice of the population doesn't to it any more than their competitor's slice it's not a big deal because they come out even. That's why they offer $10 and $20 discounts for safety and security features. It's not a big deal to the insurer since they know exactly what the "value" of each of those features is at scale but of course they want the cheaper to ensure customers so they'll toss them a small perk, a fraction of the money that feature statistically saves them.

What insurers are really scared of is when your 16yo kid and four of his/her friends drunkenly go off a cliff on their way to prom. That's hard to assess the risk of and it costs them big bucks. These kinds of oddball high dollar edge case accidents are exactly the kind that self driving cars seem to be getting into. A Tesla killing someone by driving into a barrier or semi truck sends chills down the insurer's spine because it's only a little bit of bad luck (from the insurer's point of view) away from a not so dead customer that's maxes out their collision and medical coverage.

If I were an insurer I would not be offering any automation discounts until we have more data.