San Francisco avoids this particular problem by having the walk signal turn on automatically when the car signal is green — no need to hit a button (most intersections don't have buttons at all, and the ones that exist aren't even hooked up to the light).
I don't know if this would translate well to other cities — SF has a very pedestrian-friendly layout with narrow, slow streets , small blocks, and short light cycles — but it works well enough here that it might be worth trying elsewhere.
I don't know if this would translate well to other cities — SF has a very pedestrian-friendly layout with narrow, slow streets , small blocks, and short light cycles — but it works well enough here that it might be worth trying elsewhere.