Pedestrian traffic lights: what's the point?

Pedestrian traffic lights in Boston don't work. They just don't. Yes, they do turn white from time to time, but it seems to be controlled by a random numbers generator of some kind. Or maybe it's a system with irritation-driven negative feedback. Just out of curiosity, I once spent a whole 30 minutes at the corner of Boylston and Mass Ave in hopes of getting a white light. I counted 10 full light cycles, but the pedestrian "white" was no part of any of them, despite me (and some other people) constantly pressing the button. On some other occasions, however, I did see it turn white. Go figure!

As a result, Bostonians just ignore the lights completely. The only people that I've seen patiently wait for a white light either looked like tourists or had little kids with them. And the police keeps up with the trend by completely ignoring jaywalkers. On one occasion, I watched a woman cross a street right in the middle between two crosswalks, as she stopped in the middle of the street for a nice chat with a policemen, who stood there for no apparent reason.

Ok, you want to be hit by cars, go ahead, your choice. But then, why spend your tax dollars on installing and powering the freaking lights in the first place?