And still doing a poor job of it.

You can reverse the reasoning: if you can't safely manuoever a car through a street with people, then how do you expect to do the same with a legged robot?

It's slow enough to avoid by walking around it, and you can make it small and light enough to not harm someone it might bump into.

Yes, this applies both to control-theory and to deep learning. So I'd say choose the most flexible approach, which is deep learning.

I'm not saying that machine learning isn't capable of doing these things (most of the time). I'm saying there's no way in hell you'll get a non compliant blackbox system past European safety laws.

But robots need to do more than make accurate movements. They need to detect where they can safely move. For this last part, you can't realistically make provably correct control algorithms (unless you disallow interaction with humans). Hence, you might as well use deep learning for the entire system. Also, you can limit the damage the system can make in some other way (e.g. limit the acceleration of the robot or make it lightweight, etc.)

And it has to be supervised by the driver.