Apparently, the FAA agrees, and approved an FOM that says:

"A Captain may be assigned as an augmenting First Officer on an augmented flight crew. In this case, such Captain may not occupy a seat at the controls for takeoff or landing."

So you have to wonder, why can't a captain who is apparently qualified to fly a whole trip in the right seat for time and half pay, isn't allowed to sit in the right seat on a routine no-extra-pay flight? If I'm not mistaken, the PIC captain can assign any of the augmented FOs to land for currency (or any other reason the PIC has). But not the captain? Is he not qualified? I can understand no left seat--the PIC has that, but no right seat? Why not? He's apparently fully qualified to do so.