This is a really old thread, but the subject deserves to be renewed and placed back on the table for at least occasional review.
Seemingly missing from this discussion is exactly what is permitted as a potch. Here’s my take (verified in countless discussions with rabbonim and gedolim). Virtually everything a rebbe does with a talmid MUST be educational. The rebbe is not a police officer, nor a judge. He is a teacher, one who must teach through speech and through his behavior. If he teaches a child to potch, he has failed his job miserably, and should find another career. This does not forbid the potch. It just recognizes that the potch is permitted under certain conditions. There are shelves of sforim that discuss chinuch, and the material is all easy to find to those interested in what our gedolim had to say.
Among the conditions is that there cannot be any anger at all. If yes, the rebbe is releasing his anger on a target, which is not only outside his job, but at substantial risk of teaching the wrong thing. The Brisker Rov ZT”L, for instance, stated that the first potch can occasionally be permitted, but the second one is “chovel”, an assault, and is Ossur Min Hatorah. The child must understand the potch. No “example making” is permitted. A rebbe who is unsure will not err by not potching. Discipline that is unwarranted is destructive. The inaction is not, even if it means a lesson opportunity was missed.
The SA arguments have all been chewed over. But I do not see much discussion about the result of the potch. If it backfires, it was obviously not warranted, and thus not permitted by SA. Does the average rebbe who uses the potch ever consult with a peer or superior? If not, the potch is reactive, and is not the permitted one.
Additionally, it was mentioned in a comment above, the potch is most often used in a public arena, in presence of others. There is a shame factor that is horribly destructive, even more than the smack itself. Was that part of the calculation? What rebbe is ready to assume the responsibility for ????? ??? ?????? They do take the action. But are they aware that this is not what was ever permitted?