I dunno about other carriers, but for BA it is very important for pax to sit in their allocated seats until the aircraft is airborne (and preferably afterwards).
The plain and simple reason is that we keep records of who occupies which seat. In the extremely unlikely event that an aircraft was to be lost, we (or the CAA) would be able to assist in identifying remains and/or personal property by their location on board.
If everyone has played musical chairs, then a situation like Lockerbie would become a near impossible task........yet Easyjet, Ryanair and the Lo-Cos somehow feel infallible by permitting "free seating", and still insist their operations are safe and secure!!!
Had we been made aware of this situation on a BA registered aircraft, as Ground Staff, we would have insisted on deboarding the aircraft and reboarding to ensure the pax occupied correct seats.