The "driver" (or rather "liability scapegoat") will bear the responsibility when things go wrong -- simply because auto makers or service operators have more legal resources than an individual.
Any person left to "monitor" the vehicle will not be paying attention most of the time. Even a conscientious, mindful and diligent person will tune out sooner or later; the task at hand is almost perfectly tailored to make you drift off. Maybe we can look to train engineers to see how that problem is tackled?
Further development to improve the self-driving capabilities of vehicles is likely to plateau at some arbitrary milestone, because pushing further will cost more than the court battles and keeping favour of public opinion.