Apparently Flybe do this “centre of gravity” as well. A friend of mine travelled EDI-SOU and there were plenty of seats free, but all passengers were told to stay in their allocated seats. This was on one of their new Embrarer aircraft.
When BA used to operate this route they sometimes would ask certain passengers (usually me and another Exec card holder) if we would take one of the back seats until airborne, due to there being little to no luggage at the rear of the aircraft. These were prop planes.