PJ2:
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.
I can't speak for the USAF but many decades ago when I was flying the P-2 (Neptune) and P-3 (Orion) for the Navy, there was no such thing as "your leg" and "my leg". The Co Pilot might get a takeoff or landing occasionally but just occasionally. The only time you got a landing was when there was a flight specifically designated for training. Then, the pilot making the takeoff or landing moved to the left seat. I went on a full five-month deployment without making a single landing because the squadron commanding officer decreed it. Training be damned, "safety" came first and only designated plane commanders (PC) could make landings. Apparently there was no thought as to how to handle a situation where the PC became incapacitated.
Some years later, after transitioning to attack jets, I was project officer on a weapon system which was also going to be installed in P-2s. I flew as co pilot and observer on one flight and the PC, knowing that I had P-2 experience, offered to let me make the landing. I elected to stay in the right seat and the PC was astonished. Apparently no one in his experience had ever done so. Subsequently, we were able to use the aircraft again so it must have been a really good landing.
I don't think we can make any broad assumptions about military philosophy on who is allowed to actually fly the aircraft. It varies from unit to unit.