At times, nothing slows down traffic more than a traffic cop situation of directing traffic.
First and most importantly, are the traffic cop directives superceding the traffic lights? There should be clear DOT laws on this.
The worse situations are “sometimes it is and sometimes it is not” - these scenarios slow down the traffic even more (not knowing to go on green)and some may create dangerous collision scenarios (at the interjunction where one goes on green and the other goes as well perpendiculary on the cop directive).
Traffic cops are needed mostly on jam scenarios where the cars are constantly stuck in the middle of the interjunction, stopping traffic travelling perpendicularly. This could easily be avoided by passing a law to not allow cars to cross into the box without first detecting an empty car length space outside the box - idu published an article on this years ago .