Boss's seat
I don't know about fixed-wing but I always understood with helicopters that it was because, when helicopters really came of age, flying off carriers in the Korean War, with the island on a carrier to starboard, approaches from port and plane guard to port, it made sense for the pilot, often on his own, to sit on the right. S55 (Whirlwind), S58 (Wessex), S61.
Since then, CH53, Chinook, Puma, Lynx and so on.