They had this sort of intersection (where traffic lights go red in both directions and pedestrians may cross the intersection diagonally) in downtown Washington D.C. when I was a boy (they may still do, for all I know - I haven't been downtown in decades.) They also had them in the D.C. suburb of Silver Spring MD, though that may no longer be the case.
There is an intersection not too far from me in Wheaton MD (specifically Arcola Avenue and Lamberton Drive) where the traffic lights go red in both directions, and a display counts down the seconds until one of the lights will go green again. I don't think the intersection is striped for diagonal crossing, but I wouldn't be surprised if people do so.