What I find is this. Spanking is most effective in dealing with young children. They fear being spanked. The spanking gives weight to your words. The spanking sobers and humbles the child. As children get older they get more stoic about spanking. They learn how to deal with it. The intensity of spanking required to make the same impression on a 12-year-old that you make on a 2-year-old would be excessive.
This is inconsistent with how the rod was used in Proverbs and the rest of the Old Testament: it was used primarily on the 12 and older "son."