The city I live near has walk signs come on automatically, followed about five seconds later by the parallel automobile light. This seems to be standard timing for a Leading Pedestrian Interval[1]. Because this happens in both directions it adds ~10 seconds to a roughly two-minute traffic cycle but it allows people to use the road without a beg button.

Certainly this would be a poor tradeoff in rural/suburban areas where most traffic cycles have no pedestrians or cyclists. Those use cases should use beg buttons.

But in a city where most traffic cycles include at least one pedestrian or cyclist then it seems like a useful tradeoff to increase convenience and accessibility for pedestrians and cyclists. What's more it may increase automobile efficiency as well: adding a couple Leading Pedestrian Intervals to every traffic cycle takes similar overall time than adding a full Barnes Dance[2] to half the traffic cycles. So if more than half of the traffic cycles include pedestrians crossing then everyone is probably better off with automatic walk signs on a leading pedestrian interval.

Of course if the city wants to really encourage walking they can do both and have the beg buttons trigger a Barnes dance for those who are young, old, nervous, or just need extra time to cross.

[1] https://highways.dot.gov/safety/proven-safety-countermeasure...

[2] what you describe above where all walk signs are on and all automobiles are stopped: https://en.wikipedia.org/wiki/Pedestrian_scramble