Yep. I understand that in the Canadian Forces, crews on the Argus, and I assume the Orion and other heavy transport aircraft, (C-17), switch seats depending upon whose leg it was, the PF always sitting in the left seat as commander.
Unfortunately, I don't think the philosophy you describe would be the safest in today's commercial environment where even the left seat sometimes has minimum experience and training.
Concur. Not sure even the skipper should be allowed sometimes!!