I had a water bottle fall onto my right leg while turning, this caused a sudden but short lived acceleration (e.g. 10 MpH of unexpected acceleration for less than 1 second), this was enough to cause me to mount the curb, and do some decent property/car damage (thank god nobody was on the curb). The brakes worked perfectly, and stopped the car, but it does show how much damage even a tiny burst of unexpected acceleration can do (the entire incident was under 5-10 seconds).
It honestly boggles my mind that someone can dismiss any length of unexpected acceleration because "cars [aren't] 700 hp Supras." Consumer cars are plenty powerful enough to cause injury and death due to any length (even 1 second) of unexpected acceleration at the wrong moment. Sure, if you're going straight on the freeway then you aren't going to even notice, but in a car park, while turning, or stopped at a school crossing, the brake's ability to overcome the engine are largely irrelevant since you won't be expecting it.