Interestingly, I often have the opposite problem here. The walk light turns on and I'm done crossing the street a good 45+ seconds before it actually lets traffic go. It would be nice if it somehow knew no one else was waiting to cross and let traffic go.
Of (not that I would ever do this) someone sees an opportunity and jay-walks but the walk light still turns on because they also pressed the button.
Re: Jay-walks then crossing. Some crossing and junctions skip the pedestrian stage when there is no one waiting even if the button was previously pressed. They have crossed in a gap, demand/button cancelled by detector.
The problem is curtailing the "Walk light" is that no detector is 100% reliable, so (say) if a visually impaired pedestrian is crossing and not detected, it raises as big safety concern.
Of (not that I would ever do this) someone sees an opportunity and jay-walks but the walk light still turns on because they also pressed the button.