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?