> so they should have appropriate distance from anything in front of them, and go slow enough to stop

This doesn't make sense. Crossing pedestrians go across the road, so if you are driving on a lane next to the sidewalk, then you could only go in first gear hovering the brakes, because any pedestrian on the sidewalk could start to cross the road in ~one second or less and would have right of way. Basically all streets would be zebra crossings. Obviously not how it works.