One feature about CP is unique: you can’t take it back. Any detention or suspension can be canceled instantly if the situation transpires to not be as the teacher first saw it. Not so with paddling. You can apologize for a mistake, but you can’t abolish the punishment.
Most importantly, different children react in different ways to the punishment. I wasn’t particularly ‘bad’ as a child, but I got a few tastes of corporal punishment. One was unfair and abusive, the rest were not, nor were they anywhere near so severe.