In "Talboys," the last of Dorothy L. Sayers's stories to feature Lord Peter Wimsey, Lord Peter beats his young son for stealing apples from a neighbor's orchard, much to the horror of a progressive friend who is staying with the family. However, when she later lectures the boy and asks if he is truly sorry for what he did, he replies contemptuously that he has taken his beating and that is the end of the matter. He is not obliged to listen to any further talking on the subject.
This is a large part of the positive case for corporal punishment, which is essentially the same in all the situations outlined above. It is quick, simple to administer, and easy for the subject to understand. It leaves the culprit with a clear sense of having been punished, but also allows the slate to be wiped clean, so that normal relations between the parties can be resumed as quickly as possible.
Corporal punishment can also have a simple Pavlovian conditioning effect, particularly in children who are too young to respond meaningfully to reason. If the punishment is inflicted immediately after the wrongdoing, then the person who is being punished learns to associate the two, and refrain from the behavior in order to avoid the pain.
While it is clear that some children and adults suffer negative long-term effects from corporal punishment, the same is certainly true of other punishments, such as incarceration. It is reasonable to think that a punishment which has any effect will sometimes have negative effects, which cannot, therefore, be eliminated entirely.