I do not understand why this is so hard

The point of the scriptural passages is broadly that discipline and punishment are necessary for, among other things, children - I do not think the precise means of discipline is what they are getting at. If it were, we should definitely beat our children with rods. And fools, too. The textual evidence, if we are to read it that way, is quite unanimous. Few are advocating for that. Then why be wedded to retaining the "inflicting physical pain" part of the passage? We should discipline children, hitting was an extremely common and primary method of discipline until very recently, so hitting (with a rod) is what was mentioned in the text. Hitting with a rod, in fact, seems to be the only method of discipline mentioned in the text - should it be the only method we use? Hitting - perhaps still with rods - was also the primary method of discipline in the patristic period, hence their continued mention of it when discussing discipline for children. I do not expect to go back in time and lecture St Augustine about this. But this seems to explain why hitting with rods is mentioned - not because it is the best and only way or that this specific method is mandatory, but that it was the most common way to discipline at that time (it is still widely practiced now - perhaps not as frequently with the rod, though) and - for whatever reason - they wanted to talk about discipline. But if we are going to read the injunction to discipline as requiring some use of corporal punishment, we have to go back to the plain meaning: hitting them with rods, staffs, etc, and doing so in a manner that, in modern times, may be viewed as abusive.

However, if the point is chastening and correcting the children or fools, perhaps we should instead use the most effective means of doing so. Research (here we go again) suggests that corporal punishment is not more effective than other methods and has worse side effects. "Abuse" is universally condemned. So what is wrong with this reading?

It seems some Orthodox Christians...

...really like the idea of hitting children. In case you are wondering, the recommendations of those who study that matter are pretty much universally against it. And by "it", I would note that they are specifically discussing corporal punishment, such as spanking, and specifically excluding "abuse". Here is a "popular" article on the subject: Spanking is bad for all kids I have previously shared a scholarly article, but it is dense. If you want to read that, it is titled "Spanking and Child Development: We Know Enough Now to Stop Hitting Our Children," by Elizabeth Gershoff. It is a literature review.

EDIT: the article I previously recommended was a 2010 review article, the one listed above is a 2013 review article. The 2010 was directed at policy makers in a law journal, the latter is a traditional lit review that appears to be in a peer-reviewed journal (correct me if wrong). Different audiences, also one is newer, so more cutting edge. Same conclusion: hitting kids doesn't work well, don't do it.