The number paddles serve a valuable purpose during a substitution. They indicate to the team and the scorer which player will be coming off and so make the process a little quicker and more efficient. Given that the entering player must hold it above his head to allow everyone to see, it is logical that the changeover is also made above the head.
However, it never ceases to amuse me that if there is ever a delay in transcribing the event, the players automatically raise the paddle higher, even though as soon as the players are standing together the paddle becomes redundant. The numbers are, after all, are on the playing shirts, a fact which surely doesn’t elude even the most confused scorer. And if the entering player is already on the court, the exiting player waits on the sideline those few moments longer holding his own number above his head in case by this stage anyone was in doubt.
It always makes me laugh.