build infrastructure that promotes safe driving, and
train drivers to show respect for other people on the road
However, those are both non-starters in the US. So your answer, which comes down to "at least self-driving is better than those damn people" might be the one that actually works.
What's different is driver training and attitude. Passing a driving test in the US is too easy to encourage new drivers to learn to drive. And an average American driver shows less respect to pedestrians, cyclists and other drivers, aggressive driving is relatively common. Bad drivers can be encountered in the UK of course but on average British drive better.
Huge SUV and pickup trucks are also part of the problem - they are more dangerous for everyone except people in such vehicle.
If we could do anything like "train drivers to show respect for other people on the road" at scale, then we'd live in a different world by now.
However, I used to live in a place where every local driver did an 'after you' that included pedestrians, regardless of road rules, and generally drove the speed limit (and usually less).
Both of these places in the United States!
The latter is not impossible, just rare.