There are some practical limitations, on some types. eg some Piper Seneca 1s, only had toe-brakes for the left hand seat.
I also seem to recall reading somewhere, sorry can't remember where, that only a pilot holding an instructor's rating (+ IMC/IR of course) can fly in IMC from the RHS, unless the aircraft has a full set of duplicate intruments in front of the RHS.
This seems logical to me, as I assume that instructors have been taught to read the instruments that are on the left hand side, from the RHS while allowing for the parallax.