I have Lemonade for my home insurance. It's been reliable for several years and the customer service is great. I don't have a self-driving car but I wouldn't hesitate to sign up. Their rates are very affordable.
When I've filed they just process it straight through, and then one of their actual reps emails within x hours to just check in, give an update or clarifications, etc, but that's it really.
IIRC their whole approach to competitive pricing is doing away with manual claims investigations below a certain threshold, so this tracks.