1) People would (and do) cheat at mandatory breathalyzers.
2) It's not speeding that injures people, it's the speed differences that cause issues. Limiting a car to 70mph won't help when it's icy, and they should be driving 40mph.
3) How exactly would a car detect reckless driving? How would it know that it wasn't warranted (ie swerving to avoid a kid)?
When two car are at a speed of 70mph, the maximum speed difference between them is 140mph, when they are at 50mph, it's only 100mph. So the speed of a car has a direct impact on the speed difference between cars.
We have created nuclear power plants, airplanes, giantic ships, giant dams, power grids, 2,700 foot skyscrapers, and so on. I think we can design a computer with sensors to detect unsafe driving conditions, and at least get a minimum level of operational safety.
I don't have all the answers for you. But there probably are answers, and they're probably not all that difficult, considering everything we've accomplished before. Maybe it's worth the tens of thousands of human lives to at least try, even if we don't know exactly how ahead of time.