Over the past few years in my neighborhood in Los Angeles they have been replacing the older yellow buttons (that people tend to hit 10 million times thinking it will make the light change faster) with newer ones, which are really great. When the button is pressed, makes a loud click, a red light comes on, and it stays depressed until the signal changes. They've also added in that rat-a-tat-tat clicking that I assume is for blind people. Some people still pounce the button but I've noticed most tap it a single time. I'm a big fan and I'm sure the city is too as it probably cuts down on wear and tear.
In terms of actual crossing, it is worth hitting the button at some lights, so that they know there are pedestrians (otherwise it could be a green light and you still have a red hand) and other times there's always a way for a pedestrian to cross, usually with a countdown timer after a certain amount of seconds. Every ped crossing in LA seems to have a countdown timer, which is great, for peds and even drivers (it gives you an idea when the light is about to change).
And remember, this is Los Angeles, not really a city known for pedestrians so I think the city has done a good job for the most part.
In terms of actual crossing, it is worth hitting the button at some lights, so that they know there are pedestrians (otherwise it could be a green light and you still have a red hand) and other times there's always a way for a pedestrian to cross, usually with a countdown timer after a certain amount of seconds. Every ped crossing in LA seems to have a countdown timer, which is great, for peds and even drivers (it gives you an idea when the light is about to change).
And remember, this is Los Angeles, not really a city known for pedestrians so I think the city has done a good job for the most part.