Not that I diagree it's a contrived situation but it does happen. I've seen it with my own eyes driving in rush hour traffic going between 30-40 mph and having a 3-5yr old girl run directly into traffic from the front yard of her house. Brakes were applied, car hit girl, dad ran from porch directly to girl, picked her up, rushed to hospital. I have no idea if she was hurt or not. The car clearly hit her, possibly by 1-inch meaning if the car had managed to stop 1-inch shorter maybe she would not have been hit. 30 or 60 cars were basically moving as a block down a 4 lane street (2 lanes each side). The car that hit the girl is the middle of the pack meaning the girl ran directly between cars. I was in the inner lane, car that hit girl was in outer lane (closer to houses). Somewhere like this, speed limit 45mph

https://goo.gl/maps/iDXj3wnFrhbrdzYQ8

The kinetic energy of a moving object is proportional to its velocity squared. A collision at 30mph is vastly more survivable than at 45mph.

Even if someone jumps out in front of you with no warning (which is uncommon), as long as you're paying enough attention to apply the brakes, whatever amount of braking you can do is much better than nothing. Trying to prevent accidents isn't mutually exclusive with minimizing the impact of accidents that do occur.

>This is a contrived situation that never actually happens

I have encountered this situation at least three times in the last month alone. Distracted pedestrians frequently walk in front of cars during a light change.