Self-driving is probably still new enough that insurance companies wouldn't have good actuarial data to properly price the risks, so they'd just have to charge exorbitant rates.

Companies can self insure. That doesn't mean they have to. Your accountant can run the numbers to figure out if it is worth it.

Often self insure means they still pay an insurance company to handle the paperwork, but when there is a claim the company pays it.

While I'm not sure of the specifics for car insurance.

For health care, a lot of large companies technically have say Anthem or whatever but the company pays out all of the claims and it's just administered by Anthem. So you may have seen a similar thing where all claims were handled by say Geico but it's not Geico's pot of money paying out claims.