Hmmm. That isn't really done around here, and I'm not sure it would work at the intersection in question.
The problem is that in the morning rush, westbound backs up even as-is, without the extra wait time of the eastbound protected phase.
And in the afternoon rush, northbound backs up even as-is, without the extra wait time of the southbound protected phase.
The optimum solution would be: WB and SB get the protected phases in the AM, and EB and NB get the protected phases in the PM.
I do like the idea of the thru traffic in one direction getting two of the four phases. That would certainly be a necessity here to handle the eastbound volumes (around 1200 per hour between 4 and 6 PM).
Basically, a 4-way intersection with one lane in each direction could get stuck up with left turners. Almost always, there is enough room for people to sneak around using the right "shoulder" (or parking lane, or just the mere widening at the intersection) assuming that only one car is turning left and that the car turning left is right on the yellow line to give the people behind him maximum room to manuever around. In your intersection, it seems like that may only be the case in 2 of the 4 incoming directions without having to drive on grass.
(This is standard on many single lane per direction streets here. Ofen the streets have room for parking, so there is room to pass on the right through the intersection. IMO, this is smoother than 2 lanes per direction because the cars stuck behind the left turner would have to change lanes into another lane of moving traffic as opposed to changing lanes to the parking lane just to pass through the intersection. Obviously at really busy points this won't work, like if there are multiple people turning, but when that is common, then the parking lanes get removed in favor of a proper turn lane.)
Is su;ch a movement considered passing on the right? I'm not passing a vehicle moving slowly, I'm passing a vehicle that is stopped. I beleive that if you were on a 2 lane roadway and a car has double parked, you should be able to go around a double yellow lane in order to pass the stopped vehicle (when there is no opposing traffic of course) even though it will be illegal to do that around a vehicle that is driving slow. I believe it is also OK to pass around really slow vehicles like horse carriages and bicycles.
But as far as your question about allowing a protected left at different directions at different times, that should be OK so long as you make sure not to violate yellow trap in your signaling. Since FYAs aren't used without a dedicated left turn lane, it means that the protected left must be leading. I think short signal phases would also be helpful.
I know of a few intersections like that here, but they are multi-lane and even have a left turn lane. Protected left is not triggered northbound in the AM rush, protected left is not triggerred southbound in the PM rush, at other times protected left will be triggered if there are cars in the left turn lane. Pemitted left is always permitted.
To be honest at that intersection, there aren't too many turning left anyways, but they did not want any time taken away from the dominant movement of rush hour traffic.
https://www.google.com/maps/@39.0274704,-77.0765594,3a,75y,215.98h,88.07t/data=!3m6!1e1!3m4!1s70Qg62PIt0qMIJFhC0erHg!2e0!7i13312!8i6656?hl=enConnecticut Ave and Knowles in Kensington, MD. Sign reads "Left turn arrow does not operate M-F 7-9 AM". On the opposite side it reads ""Left turn arrow does not operate M-F 4-6 PM"
