Back in the 80's I flew with an european airline, B732, where PF flew LHS. i.e. an F/O flew as PF in LHS. The captain in RHS had dual controls and a tiller (I think). It's a bit like a driving instructor, except they don't have steering capabilities, usually only stopping. It was exactly like it was in flying school. The QFI flew RHS. No-one ever thought that was weird.
The concept was, the B732 was so basic in flight-deck layout that is was designed to be flown from LHS, not RHS, so an F/O, of suitable experience, was checked out in sim as PF LHS. I don't believe there was ever an issue with it. The A/P control and other systems/displays were orientated towards LHS. It seemed basic sense to them.
Later, when they upgraded to EFIS a/c. and the flight-deck & A/P was orientated equally L & R, the practice was no longer approved. Naturally the F/O's were miffed, but quite quickly it became forgotten.
LTC's with F/O's under command training fly PM & PF in RHS. Why is it considered such a big deal?