Pretty sure that's just an asshole thing, not a "local quirk." It's like saying not using your turn signal is a funny quirk of BMW drivers, or going 55 in a 70 in the left lane in a Prius.
Typically, the "Pittsburgh left" is used in places where there should be a protected left turn as part of the signal cycle, but there isn't, and at times of high traffic flow it's the only way for any traffic to complete the turn (since waiting for oncoming traffic to clear on a green essentially means waiting until the multi-hour-long period of high traffic is over).
My point was, why do you need to do that when you can just enter the intersection during the green light and complete your turn once the light turns red?
Then the laws in Pittsburgh are just bad. Not a design question at all.
Here you oull into the intersection on green, turn slightly ti a big white cross on the road for exactly this purpose and go when it is clear. This happens when the oncoming side has red, but before the crossing cars have green. The time between red and green is long enough for all two or three cars to clear the intersection.
Get better laws i guess?
Which is why you need to move onto the intersection as the light turns green -- you've now passed the traffic light, so once the oncoming traffic gets the red light, you are clear to turn.
As someone else pointed out, you can do three right turns instead.