It should not be allowed to have both the pedestrian crossing and the turn signal showing green at the same time. The turn signal could switch from red to green immediately after the ped-crossing turn red, but no sooner.
If they want to increase the flow of the intersection, they could have the turn signal be red-less, as in not having a red state. Then when the straight-ahead signals go green, it would be allowed to turn left yielding to oncoming traffic and any pedestrians in the crossing. Then when the oncoming traffic and the ped-crossing have turn red, the left turn signal goes green indicating free path.