FSD in its current form is no different than cruise control or seatbelt function, a Level 3+ system operating within its OEDR is a different story.
I'm not aware of any "liability problem" though in the way you're spinning it, everything in terms of liability seems quite clear. You don't own the driving task when using a Level 3+ system within its OEDR, something Level 4+ might not even have a steering wheel or pedals. It's like hopping in a Waymo or Cruise except you own the vehicle itself, but you aren't responsible for what the vehicle does when the system is operating.
The only problem I see is the manufacturer feeling comfortable taking on the risk, which would be why Tesla needs the system showing levels of safety/reliability far in excess of human drivers. If FSD was merely as good as the average human driver and all accidents were now owned by Tesla, I think they'd have a bad time.