I am not a traffic flow engineer, but I have experienced what you describe in regard to the walk button behavior in many places in western Washington, US. I always reckoned that they were using a simple model in which a button press would cause the "WALK" signal to always be fired at the corresponding light configuration at the _next_ cycle start. This is most likely a safety consideration because, as you noted, there may not be enough time to safely cross.

In some complex intersections I've noticed that the 'cycle start' doesn't necessarily line up with the corresponding configuration for the walk button which was pressed. This may result in having to wait nearly two complete cycles for the walk signal in the worst case (pressing the last configuration's walk button immediately after the cycle start). The resulting behavior could be considered a bug, or perhaps just more consideration payed to vehicle traffic. But it is certainly frustrating as the pedestrian.

At many intersections I cross now the signals are automatic with the traffic flow. Most of them also contain a countdown timer indicating the number of seconds until the light changes. It seems that this behavior would be a good tradeoff for pedestrian efficiency and safety. However it comes with a bit of trust from the gov, that you know you can't walk across 5 lanes in 2 seconds.