Well, there are already companies that accept nigh-unlimited liability for the consequences of car accidents - insurance companies. And drivers are used to paying enough in insurance premiums to cover the costs of the payouts.

Accepting liability for car accidents isn't necessarily a death sentence for a car company, any more that it is for an insurance company. Just instead of paying a $x00/year insurance fee you'll be paying an $x00/year self-driving subscription fee.