The main disadvantage of supersedure (from the beekeeper point of view) is that the bees are choosing the queen rather than the beekeeper.
The colony may have heritable traits which you don't want to propagate.
Also, if you keep a pure race of bee and they supersede the queen you may well end up with a new queen mated with mongrel or different race drones which will be an unknown quantity in terms of temper and handling.