In most states, cars themselves don't have many requirements/checks post-sale. Some states check that emissions equipment is still functioning, but because this is often done by third parties, cheating is rampant. Still some states require safety inspections, but that is far in the minority.

ADAS systems are mostly legal because they are officially "assistance" systems, and the driver is still responsible for whatever the vehicle does. There is exactly one commercially non-assistance "self driving" system that I am aware of in the world, and it's made by Mercedes Benz, and is only operable in very specific situations. MB takes responsibility for what happens when the vehicle is operating in this mode.