Cars can stop in quite a short distance. The only way this could happen is if the pedestrian was obscured behind an object until the car was dangerously close. A safe system will recognize potential hiding spots and slow down preemptively - good human drivers do this.
"Quite a short distance" is doing a lot of lifting. It's been a while since I've been to driver's school, but I remember them making a point of how long it could take to stop, and how your senses could trick you to the contrary. Especially at highway speeds.
I can personally recall a couple (fortunately low stakes) situations where I had to change lanes to avoid an obstacle that I was pretty certain I would hit if I had to stop.
While it's true they don't stop instantaneously at highway speeds, cars shouldn't be driving highway speeds when a pedestrian suddenly being in front of you is a realistic risk.
I don't think these problems can just be assumed away.