About the crosswalk thing, I'm pretty sure that's a myth. At least everywhere I've lived if you don't press the button, you don't get a walk sign. There are intersections that have walk signs automatically, but they don't have buttons.

It's the same for door-close buttons in the handful of elevators I use regularly. The doors do close just when you push it, whereas you have to wait several seconds if you don't.

Depends, in my apartment the door close button is actually counter productive as you have to push it all the way until the door closes. As people tend to only push it quickly, it actually opens the door which was already closing.

Pretty annoying.

This is also the case where I live - if you don't press the button the whole thing stays unlit so you know it's "off".

There are busy intersections where the buttons are installed, but are only active outside of rush hours or on weekends or not on weekends or only when the circus is in town etc.

Because the programming of the lights is different to facilitate maximum throughput (f.e. with a green wave) in some periods, and the walk signs are on a constant/different timing then.

I hate, REALLY hate the intersections that try to be smart about me taking a kitty-corner crossing by pressing both direction buttons.

When I do that, I'm trying to tell the light what I need so it can figure out the correct timing signals to get me where I need to go faster.

Yeah where I live, if there are no cars the lights don't change.

Door close buttons do close the door, but any time a normal person is using it, the door is already about to close as fast as it is allowed to when you press it, so it's not going to close any faster. If you're a maintenance worker however, who uses it outside of normal operation the door close button has to shut the door or it won't shut until you put it back into it's normal operation loop, and also because if it doesn't shut the door it will fail a fire test.

A bit like those temperature dials in hotel rooms.