If there were limitations on where the P1 should/can sit they would be in section 2 of the POH and for tailwheel aircraft there is often a 'This aircraft must not be flown solo from X or Y seat' statement in there.
Not found one yet for your average training aircraft...
As has already been pointed out instructors fly from either seat without any insurance issues and often I sit RHS when flying solo as it's my normal perspective.
Also as has already been said - sort out who is P1 (and make sure they're covered from an insurance point of view) and THEY sign the techlog prior to departure.