I think it might be relevant to point to the first volume of the actor David Niven’s autobiography, “The Moon’s a Balloon”. I don’t have a copy it to hand at the moment, but my recollection is that Niven was caned at school on a number of occasions. Several of these punishments were given at a prep school, by someone who could only be described as sadistic in the extreme. I can’t recall whether Niven ascribed any improper motives to these punishments, but I wouldn’t be surprised if he did.
Later on, Niven moved to Stowe, a public (US: private) school; this would have been in the 1920s. On one occasion there, he was caught cheating with a friend in a public examination and was hauled before the headmaster. He said, in the book, something like “X’s beatings were rare but legendary”. Niven was given twelve strokes of the cane, and although he managed to keep quiet during the punishment, he ran into the nearby woods screaming his head off.