Some lights have separate segments where it's only straight or only left-turn. Pedestrians only have the walk sign during the straight traffic.
True but it is uncommon. It is indicated by a *red* left arrow light. I think that works.
However if there is only a green left arrow light that turns off when opposing traffic starts moving, you are still allowed to turn left, though you have to wait for a gap in the oncoming traffic. For obvious reasons (the driver is looking only at the oncoming traffic) this is when the pedestrians are hit.