I'm going off of research. Physical punishment of the child is dangerous on a societal level because most parents end up getting emotional. For example read this

Interviews with physically abusive parents about the abusive events for which they were referred to child-protective services expose a startling and compelling theme: Nearly two-thirds of the abusive incidents began as acts of corporal punishment meant to correct a child’s misbehavior.49 The authors of a review of 830 substantiated cases of abuse observed that “no factor was so universal, so ubiquitous, as some identifiable behavior on the part of the child which precipitated the parent-child interactional sequence culminating in abuse.”50 A review of physical-abuse cases in the 2003 Canadian Incidence Study of Child Maltreatment revealed that seventy-five percent of these substantiated cases were intended by the parents to be corporal punishment.51 Similarly, an older review of maltreatment cases in the United States found that sixty-three percent of the incidents of physical abuse developed out of intentional corporal punishment.52 A study of abusive parents in Mexico found that these were more likely than a group of comparison nonabusive parents to use conventional corporal punishment (for example, spanking or slapping) and to use more-severe methods (for example, kicking, biting, or burning),53 which suggests that more-frequent and more-severe use of corporal punishment makes physical abuse of children significantly more likely.

Vast majority of "abuse events" start with what was intended as simply corporal punishment. This is the crux of the problem. It's hard to separate the effect of mild and conscientious punishment versus what often ends in abuse.

Which is why it's easier just to say "corporal punishment is bad" because it will dramatically reduce the rates of abuse in society.

But there's more nuance to it. Corporal punishment tends to not be damaging depending on frequency & intention of the parent. If the frequency is low (<5 times a year) and there is a feeling of warmth between the parent and the child, the kid doesn't experience a meaningful mental health impact. However, in every other case (vast majority of cases) there are negative mental health impacts. Higher rates of ADHD, misbehavior, future addiction issues, etc.

Which is why the advice "don't spank your kids" is a good one because you simply can't trust every parent to be a fully rational actor with the long term perspective of their kids best interest in mind. Just safer not to do it.

I wouldn't do it either