That already is happening. https://en.wikipedia.org/wiki/Self-driving_car_liability:

In 2015, Volvo issued a press release claiming that Volvo would accept full liability whenever its cars are in autonomous mode.

[…]

Starting in September 2023 in the United States, Mercedes-Benz takes liability for the Level 3 Drive Pilot as long as the "user operates Drive Pilot as designed," but "the driver must be ready to take control of the vehicle at all times when prompted to intervene by the vehicle."