I can't count the number of commercials I've seen for Fords and Nissans and Subarus and every kind of modern car that has this exact feature, and this is exactly how the advertising plays out. Someone sprints in front of the car, the car stops automatically, everyone is safe, pedestrian continues with their life. I've never used it in real life, but I assume it works how the ads show it.
If Uber can't match a $25,000 off-the-shelf floor model mass-market midsized sedan for collision avoidance, it's hardly a self-driving car.