Even if the guy jumps in front of your car? What kina bs is this? Perhaps peds need to mind their surroundings as well? Because cars can't stop instantly you know.
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.
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.