Right on red is (or should be) never allowed during a pedestrian scramble. That's just asking for trouble. The box must be entirely clear of cars during the walk signal.
The other great benefit is you can cross the diagonal (kitty corner).
(I'm also amused at the idea of making a beg button for cars. Maybe make cars have to text a phone number to beg the light the change. If cars had less annoying to the neighborhood horns you could have "horn recognition" and use the horn as a universal button.)