Technology improves and evolves. If it didn't you wouldn't be so reliant on Google Maps. We convince people of progress by a safe track record. Google maps may fail occasionally but more often than not it gets you to your destination at the estimated time.
Yes self-driving cars can't be "more often than not" safe. But starting with smaller areas and showing the difference it makes on people's lives and the environment can be a good start.
I ask this cause my wife's previous phone had consistently crappy GPS performance, losing satellite connection very often, getting stuck etc.
I never had such issues with mine, nor with her new one.
Unless you get a DGPS unit (super expensive and require 3k subcription from satellites) you get north of 1m accuracy.
When I raved about self driving cars to my wife, she said to me: look, Google Maps is messing up on a continuous basis (GPS errors, software errors, bad routes, mapping inconsistencies, underestimated ETA). If they can't make a decent GPS app, how could they make a self driving car?
I had no way to counter that. It's true, GPS is an old tech purposefully dumbed down for non-military applications. But how can we convince people of progress when it is so lacking?