If the car is not able to safely operate without constant human involvement then it definitionally requires a person on board.

If losing cellular service causes it to stop, then in emergencies you're pretty much guaranteeing a large number of roadblocks for emergency services, on top of their existing hazards to emergency services when operating in ideal environments.

> Should the car keep going when it is not confident to do so?

See above, re: if your car can't even pull over and park safely on its own it has no business being on the street.