I think there will actually be a couple interesting adjustments/market forces acting in the car companies' favor.

First, if the insurance applies to fully autonomous driving only, then I suspect they’ll reach a point where the cost of insurance+automation ends up being less than just insurance through third parties.

Second, cutting into the traditional insurance market share is likely to increase costs for those who remain on traditional insurance, assuming there’s a significant enough number of people jumping ship. Combined, this creates a huge incentive for more users to jump on the self-driving bandwagon.