We cannot know if the push-button crosswalk buttons work when so many of them are broken.

That's right, NA:

We're fundamentally better.

Jeff Speck, who once authored a walkability study for New Albany -- a document now being depleted, one precious page at a time, as toilet paper in Jeff Gahan's mayoral washroom -- is quoted here on the topic of push-button crosswalk signals: How Push-to-Walk reduces the quality of walkable neighborhoods.

It is almost always the cities with push-button crossings that need the most help ... push-buttons almost always mean that the automobile dominates, as they are typically installed in conjunction with a new signal timing in which crossing times are shorter and less frequent. Far from empowering walkers, the push button turns them into second-class citizens; pedestrians should never have to ask for a light.

And boy, does the auto dominate in New Albany.

There is reason to believe that quite often, push-button at crosswalks do nothing, and in fact are virtual placebos.

MANY CROSSWALK SIGNAL BUTTONS DON’T DO ANYTHING ANYMORE (Today I Found Out)

Does pressing the pedestrian crossing button actually do anything?, by Tom de Castella (BBC News Magazine)

My sense is that in New Albany, these push-buttons are enabled and actually do something. I base this observation on lengthy waits at crosswalks downtown, where the buttons (as the one pictured above) chronically malfunction.

There are a great many of them.