I bet it'll be more about money than lives. As soon as car insurance is an order of magnitude more expensive when "driving yourself", then we'll have self-driving cars as default!
It's not like that's going to happen next year or ten years from now.
Insurers like boring, happens at a consistent rate, human error accidents so long as their slice of the population is not making them at an appreciably different rate than the competitors' slices.
Insurers really don't like hard to predict accidents that cause people to max out their collision and medical (which is exactly what would have happened in the Tesla cases had the customer not died) which is exactly the kinds of accidents self driving cars seem to be having.