I don't think it's an obvious conclusion that error bounds aren't important for automation because they aren't calculable for a human. They are just very different beasts.
Let's do a thought experiment: let's say, we had a self-driving car that's verifiably 10x better than human on average, yet does not provide "error bars". I know we don't have one now, and unlikely to have one in the foreseeable future, but bear with me here, for the sake of argument.
Would you trust it, rather than a random human Uber driver?
FWIW, I'm amazed that driving cars manually is perceived as normal every time I drive one. I can easily accelerate 2+ metric tons of metal to 100+ MPH, and get distracted, launching this deadly projectile with me inside into oncoming traffic. Most roads have _no dividers_. This does happen from time to time, lots of people die. Nobody gives a shit.
Humans suck so bad at so many things that robots will be better than them at a lot of fairly unconstrained tasks in the next decade or two. And I'm pretty certain they won't have error bars while doing what they do. Humans don't.
Note that X doesn't need to be high, or higher than a human, for example a self-driving car with a 60% failure rate is fine as long as we know when and how it fails. It's this "when and how" that's completely missing from self driving cars.
And in machine learning in general we just don't have any guarantees that a model trained on some dataset will perform the same way in the real world.
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.