Interesting point about the delay before a private whacking being a way of making the punishment more serious. I can see that that would be so – waiting a few hours or even a day or two knowing that you were going get a very sore bottom after a swishing from the headmaster would no doubt be an uncomfortable experience in its own right.
If I think back to situations where I was told to report to a master at some later time for what I assumed would be a good slippering (or perhaps even the cane once in the case of the deputy headmaster) I was certainly apprehensive.