I wouldn't call it larger safety margins. Many if not most of the cases where car drivers should take action are survivable if they don't; that's different for pilots in airplanes.
Pilots typically have more time to react, though (astronauts lie even further away along this axis; in cases where astronauts can take action to save their lives, they typically have even more time, but also, in many cases, there's no action that will save them)
As to the "take control at a moments notice": that's where the problem lies.
The arguments in "Ironies of Automation" (https://www.ise.ncsu.edu/nsf_itr/794B/papers/Bainbridge_1983...) such as "By taking away the easy parts of his task, automation can make the difficult parts of the human operator's task more difficult" haven't lost any of their power in the 30+ years since it was published.
Because of that, I doubt the typical driver will be able to handle emergency situations, as it will require frequent training.
No, it's a problem with automation that has been well-known since the 1980s. There is not an easy solution to it.
If you have a human-supervised safety-critical automated system (where "difficult" situations are to be overridden by the human) you end up needing the human supervisor to be much more skilled (and often faster-reacting) than they would have needed to be just to do the operation manually.