Most of them do not work, this 8 year old NYT article claims that 120 out of 3250 signals in NY work a decrease from their census in 2004 and mentions how a different agency found 1 working button across various cities. The only ones that kind of work in my experience are in New Jersey, where if you do not press the button, the intersection will never clear you to walk. The signals and everything work the same, just you will never get walk at the intersection (even when you normally would have) without pressing the button.
They work in my town just outside a large metro area in the US.
That said, no one seems to actually use them here and are always crossing traffic at the worst times.
It’s really frustrating to watch people of every age playing chicken with cars daily.
If people are frequently crossing between crosswalks, there probably aren’t enough crosswalks. If they’re pressing the buttons but crossing before the light changes, even if the buttons do cause the lights to change eventually they’re probably set up incorrectly and make wait times too long.
It took me 18 months of back and forth with my city to get them to fix a particular light. The beg buttons technically worked, but the light is where a major street intersects with a residential street, and all the beg buttons would do initially was make the pedestrian lights turn green the next time the lights changed. Problem was, if it didn’t detect a car there it would never trigger a change. What finally got it fixed was me sending the city council an 8 minute video of me waiting for the light to change before a car came along.