Safer drivers I believe, but how do you get around the uncapped liability the service provider carries if someone gets hurt?

The same way you do it with human drivers is one option. I.e. mandatory liability insurance.

	▲	close04 19 minutes ago \| parent [-]
		Human drivers pay one insurance, for themselves. It’s easier to swallow because most drivers think they are above average skill. Not so easy when they need to cover someone else’s coding mistakes. And if the company has to pay for every car that self drives that can get ugly fast, one bug and half the fleet has a fender bender.