The same thing happened with elevators. When they had operators who would physically make the elevator move and then these new fangled "magic" ones came in people freaked out, got used to it and now no one cases.
I get the feeling the it's the same way with cars just an order of magnitude bigger of a change since they're such a part of our lives.
But that also provides evidence of the parent's point that "Most of us are going to expect nothing short of perfection from these machines to really trust them."
We absolutely wouldn't be OK with elevators that now and then fail in a dangerous way. Doesn't mean it never happens but it's considered to be someone's fault when it does.
Elevators do fail occasionally. There are several videos of elevators moving before the door has finished closing, or stopping mis-aligned with a floor. It's just a very unusual occurrence.
I get the feeling the it's the same way with cars just an order of magnitude bigger of a change since they're such a part of our lives.