Liars! LIARS! You lied to us making us think that the crosswalk buttons actually do something! But they don't. So, you are about to cross a zebra crossing and you press the button on the traffic light, and what you expect is that after a period of time the cars will stop for you to cross. This used to be true many years ago. But these days, traffic lights are all connected to a timing system optimized to have the best traffic control. So, the crossing light will turn green for humans in specific times, regardless of how many times you press that silly button.
These are called placebo buttons (like the placebo effect), simply because they make you believe that they do something. Other examples: The "close door" button on the elevator and the thermostat on public buildings.
But we still press these buttons. And i bet that if you go right now in a crosswalk and see this button there, you will not resist and you will press it thinking that "maybe this one still works". Why? Over the years, our brain has been programmed to believe that pressing a button will definitely do something...
Well, "close door" button on elevators and the thermostat on public buildings work. At least they work for me when i play with them.
But the crosswalk button, i agree with you. I have one close to my house and... it's a waste of time. For sometime i was trying to find a pattern, but there is nothing to find. It's a fake.