So far, while self-driving cars have been in accidents, all of them have had it discovered that the accident was caused by the driver taking over from the system. That's pretty promising on it's own. Notwithstanding the case where a Google car pulled out in front of a bus trying to drive around sandbags, but given that was after 1.3 Million miles, that's still a fairly good track record.
Just being a pedestrian I've had a few encounters with cars nearly hitting me at crosswalks or intersections because the driver wasn't paying attention. Usually it's some idiot glued to their phone. I'd rather a computer system that was always paying attention than a person who almost never was.
If we're at a crossroads when it comes to self-driving cars I think the ethical "trolley problem" we have is deciding between not working on and implementing self-driving cars and continue on with all the preventable deaths we have today due to car accidents, or make car travel universally safer at the cost of letting an AI make a few moral decisions.
I think in some sense it's a cognitive bias. We think of things "keeping on as they were" as being normal, and therefore people dying because things remained unchanged were totally natural. It's why accidents involving self-driving cars are so newsworthy- they reaffirm our cognitive bias that nothing should change. It's the same reason that accidents involving cars rather than carriages were newsworthy around the time of their original introduction, when "high-speed chase" meant a bicycle- or accidents involved people rubber-necking one of the new horseless carriages and not paying attention, which we also see with self-driven cars which have no driver occupant.
So far, 99% of the information leans in that direction when it comes to self-driving cars versus cars driven by their human occupants. I'd argue that we have all the information and acting on it to make travel safer for everybody is almost an ethical obligation to develop and make the technology available at this point.
Self-driving cars cache information and can observe their surroundings. They don't rely on an Internet Connection to work.
Self-flying aircraft is already a thing but I don't think it will be a thing for commercial airlines anytime soon. The advantage of self-driving cars is a reduction in accidents, injuries, and deaths, but there isn't nearly the potential to see those sort of improvements from a fully autonomous 747 for example.