Are you asking why peds are required to press a button at some intersections for a walk signal?

If so, consider that some intersections may require a long time (~45 seconds) for a ped to cross. When no one is crossing, this may be sub-optimal and a shorter time for that specific light combination should be used.

Nobody should have built an intersection anywhere that big, then. But such behaviors are totally infuriating in places where there are many pedestrians, for example all of the stations on the SF Muni's T-Third line require passengers to push the button to cross the street after disembarking at center platforms. These crossings are not far (only half of a moderately wide street) but they don't have a pedestrian walk phase by default. If you haven't pushed the button you get to just stand there for another cycle. Example:

https://www.google.com/maps/@37.790723,-122.390108,3a,75y,92...

As you can see, the street-view car has captured a brilliant scene. Traffic is jammed. Many pedestrians are waiting to cross. The guy in the Mini is either going to run the light or stop in the crosswalk. The person in the white minivan has somehow managed to drive up the street car tracks. And for the topping, someone has blocked the bike lane with a portable sign.

I'm asking why, if the lights will cycle in such a way that pedestrians COULD cross, why they should not automatically allow pedestrians to cross. It's infuriating to miss a cycle as a pedestrian, and whom does it benefit? I'm not suggesting that there not be buttons which can force a cycle or accelerate a cycle. How would motorists feel if traffic lights defaulted to red?

I haaaaate that. Arlington, Va has some, but only some, crossing that do that. Sometimes I'm waiting around for 2 cycles before I realize.