What makes roads safer is better engineering, better technology, and education.
I did my dissertation on this. I was surprised at the amount of tautological reasoning when I reviewed literature: traffic enforcement good because traffic enforcement, or speeding bad because speeding.
No, something’s bad when it causes harm, and something’s good when it has a net benefit, and the published traffic-safety research focused on laws and enforcement is too often shoddy.
In my mind, education is by far the biggest issue today. Most people have no clue about vehicle dynamics, or they think bad stuff only happens to other people. Like you said, speed itself isn't necessarily bad. But people speeding around a turn have near zero chance at avoiding a bad outcome if there's some obstacle in the road - they've never tried to slam the brakes on while turning, and/or they think there couldn't possibly be a disabled car, a person, a deer, etc around that blind turn.
Technology has certainly helped improve survival. I think it is helping to prevent some accidents to too. I think we still need some refinement on some of the newer tech and/or better education on how to use it. I think sometimes people rely on the tech too much, like autopilot. I think many people aren't fully ready to take over if autopilot has an issue. I had two friends using autopilot tell me it slammed on their brakes at an overpass shadow. Now, they didn't go into detail about the time to recovery, but I'm guessing for at least some people it's significant if they aren't paying attention because they trust the system too much.
As for engineering, there's probably a lot that could be done. I haven't seen many changes to road design beyond adding stop signs, lights, textured pavement on turns, etc. I'm guessing it's cost prohibitive, similar to how educational changes are socially prohibitive.
How so? Don't you want to see some competency exhibited by people before they drive[1]?