In the UK when there's a green man (pedestrian crossing signal) it means that all traffic is stopped, and (though not officially recommended) you could cross diagonally and it'll be fine. In the US and some other countries, it doesn't seem to have that meaning, so other traffic may still have a green light or be allowed to pass a red light where pedestrians are being told it's safe to cross.

Pedestrians very often get the green walk sign at the same time as cars in the same direction get the green straight ahead sign that implicitly allows right turns as well. In that scenario, the cars are often located just behind the pedestrian’s peripheral vision, and the cars are looking up and ahead at the light

It seems to me that that's the wrong way round, if there's no pedestrian crossing it's safer to cross when the traffic is moving from the left-right of you than in front and behind you.

My suggestion is that pedestrian crossing signals should stop all car traffic in the junction and if no signal exists the guidance should be to cross where the traffic is visible (left and right) not when it comes from behind you.