It is probably possible to get drivers to improve if the incentives were there or if they had no choice due to external factors. I bet it would be cheaper than money spent on self driving tech too.
Drivers can improve, but they won't. They will talk about the abstract just fine, but always in context of how "the other guy" is so bad, they resist any suggestion that they might not be good either. As soon as your point out something that nearly everyone is doing wrong (as backed up by statistics and traffic safety engineers who study this) and suddenly they will shut you down. As the other reply said: drivers vote and so any change that would affect all of them is impossible.
I'd love to see better public transit, but transit is so bad for most of us that it would take a massive investment before there is any return, and half measures won't work. You have to go all in on transit before you can see any significant change - if you invest in the wrong network you won't know until a massive amount as been invested and there is no return (leaving open the question of if a different investment would have worked).
If only we honked the horn when our cars are stopped, to let people know where it is. And honked before putting our cars in motion, to let people know we're about to move. And while the car is in motion, to let people know the car is in motion. I saw no collisions while visiting India, and continuous honking must be a significant part of the reason.
True, the UK is basically an alien civilization compared to the average american state. No comparison is meaningful unless we compare it to every nation state in the world.
Deaths and accidents are different measurements. Cars are much safer in an accident than they were in the early/middle 20th century.
Per-mile-driven deaths started climbing again around 2012 in the U.S., I'd wager due to the trend towards larger vehicles causing more collateral damage.