Imagine a game of Russian Roulette with one bullet in a gigantic chamber (N slots) where you get to win a small prize every time the gun doesn't fire. Is there any sense in asking if there is a N large enough to make you consider playing this game consistently for 2-3 years, when the gun is pointed at your kids?
Mind you, I am not defending helicopter parenting and I do believe that we should err on the side of autonomy vs safety. But I can think of other ways to exercise this autonomy (e.g, drop the kid at the door of a local supermarket and say "here is 10€, can you please go get X, Y and Z while I am outside looking for something else?") without worrying about is the worst possible thing that could happen.