Why do airlines require passengers to return to their allocated seats for landing?
Its a matter of legal requirement (under the FAA, and I presume the EASA has a similar reg). Strictly speaking its really more important that the passenger returns to a seat. Generally you are asked to return to your seat as it can be assured its empty and available for you. Under FAA regulations you are required to be wearing a seatbelt for landing and thus must be in a seat 


  14 CFR 121.311 - Seats, safety belts, and shoulder harnesses.
  
  (b) Except as provided in this paragraph, each person on board an
  airplane operated under this part shall occupy an approved seat or
  berth with a separate safety belt properly secured about him or her
  during movement on the surface, takeoff, and landing. A safety belt
  provided for the occupant of a seat may not be used by more than one
  person who has reached his or her second birthday.


Weight and balance is important but not on a single passenger level i.e. on an airliner of decent size if a single passenger moved around it would be ok. If half the plane was empty and the passengers rearranged them selves there might be an issue.  


  How do airlines which do not allocate seats to passengers satisfy the
  same requirement when there is no published seating manifest in
  advance of passengers entering the aircraft, or why are they exempt
  from such requirements?


They are not exempt from the requirements but there are enough seats for everyone on the plane and as noted above its really important that you are belted in so taking an available seat will do in this case. On these flights generally speaking, you take a seat prior to takeoff and that somewhat becomes your seat for the flight. In my experience there is little if any mid-flight seat swapping.    


  Furthermore, in the event, only one member of the couple returned; the
  other remained in the non-allocated seats (an example of
  non-enforcement).


As noted above the policy is to be belted in, so the regulation was indeed enforced. The other member of the couple may have remained in the seat if they were the only person capable of preforming the exit row duties.