I think a lot of the nuance has been lost here. Even throwing around phrases like "10x better than a human" is already implying a lot of very vague measurement or knowledge. In what ways, and in what environments, is it better?
I've dipped my toes into robotics a few times, and every time I end up being reminded of just how painful it is. Even when you're working in an idealized simulator, it's extremely easy to find a little edge case that causes completely bizarre behavior. And moving out of the simulator only makes things far, far worse.
It's really easy to forget about those sorts of details and brush it away as just things to be solved while developing the automation. But they don't just go away so easily. Error bounds are there to help manage these issues and ensure we know how to best use the automation.
In many instances I think people would tend to prefer the Uber driver in a moderate reading of your scenario. A human driver is likely to perform somewhat consistently and predictably. If they drift around the corner and leave a long skid mark in front of your house you can make some assumptions about how they are going to drive. If you get in and see them struggling to keep their eyes open, you can again make some assumptions about their performance. A well-rested and safe driver is extremely unlikely to suddenly throw themselves into on-coming traffic with no warning. You can refuse or stop the ride if you judge you are not safe.
Automation is a different beast. It's liable to fail in ways that a human driver would not. It may be performing wonderfully until something a human would not even notice happens, and which point it may indeed throw you into on-going traffic. For example, look at adversarial examples in deep learning. As a passenger in this case you don't have a way to judge your own moment-to-moment safety. Even if it is safer on average, the sheer unpredictability and the resulting stress is likely going to eat significantly into any gains.