> why should s/he wait to cross the street if s/he knows that the car that is nearing has an anti-collision/auto-break system

I would highly recommend visiting Cairo in Egypt and crossing a busy road: With a swarm of cars going left and right, you simply 'pick a car' by looking directly at it and step out into the stream of (multi-lane) traffic. It's freaky at first, but it slows, moves and bends around you as you walk across the road. I've seen mothers with bags and children doing this at even busier places.

It seems that here in the west, when we're driving, we have a 'get out of my way' mentality that seems out of proportion with how we walk down a pavement. ie, As we walk, we move and flow around slower/oncoming people -- we certainly don't shout at fellow pedestrians to get out of the way and then barge them out of the way when they don't.

Edit: A video of cairo street crossing https://youtu.be/qYjiO_kLYKY