I think they are meant for people to believe they do something so they’ll feel better and wait. I used to walk a lot and encounter lots of crosswalk with buttons and I got used to how fast I should go in order to catch green every time and I could predict when the next crosswalk was going to turn green. If they truly worked then they should have been out of sync. I never pushed the buttons and I saw the light turning green even though no one pushed the button, if the buttons worked then why would the light turn green?
I also asked gemini about this and he said I’m not going insane, strange because I never mentioned if I was insane or not, but good to know I’m not.
Maybe some buttons work and other don’t depending on where it is?
This is usually also tied to timing, just not in the sense people hammering the button to cross the street faster want. Without pushing the button, the lights will change based on car availability. Pushing the button often won’t get the light to change sooner, but it will likely stay longer to allow for people to cross the street.
It may have done that regardless due to traffic patterns, but the button guarantees it has a minimum safe crossing time.