It strikes me that a useful analogy here is the adoption of automatic elevators in buildings. In some ways, it's amazing that pretty much everyone in industrialized countries is OK with being locked in a windowless box controlled entirely by a computer, hanging over a hundreds of foot deep shaft, and in fact many people were terrified of that when Elevator operators were first replaced with computers. Some places even had operators employed to simply stand there and push the buttons to provide confidence that an trained expert was there, even though they didn't actually contribute to safety. Eventually, autonomous elevators got common enough that people will look at you really funny if you're not willing to ride in one, even though they are still responsible for ~20-30 deaths per year.