There will always need to be a "wasted" step. The hanger comes off the rack with the hook away from the robot and has to go back on that way. Since there are two shoulders of the hanger to put into the shirt, they have to hand the hanger to from one to the other, and that would leave the hook facing the last robot if they don't do this extra step.
I don't see that it helps, since the task is symmetrical. Whichever arm takes it off has to give it to the other arm at some point so both sides of the hanger are used, and it needs to be given back either before or after doing the hanging so the hanger's hook is back on the outside (facing away from the arm holding it), before replacing it on the rack.
Would be interesting to know if the AI figured this out (the hard way, I'm sure).
Not sure we are talking about the same thing. I'm specifically talking about 1:07-1:10. What is the reason why the left arm could not take the hanger off directly, without involvement of the right arm?
It could, and then the hanger would be facing the other direction, and everything would simply be mirrored left-right. The last arm to hold the hanger still has to replace it on the rack, which means it needs the hanger's hook facing away from it, which only happens when there have been an even number of exchanges between arms. Thus the need for that extra exchange.
That extra exchange could have been done after putting the shirt on the hanger, but that would have been more risk for it falling off again.