I do think it would be important to understand the definition of corporal punishment. It is in not difficult to understand how a beating versus a smack on the rear are not the same.
I should also add, I have always believed that if you have to hit a kid repeatedly you suck as a parent.
I absolutely agree with both of your points. I would add that there are some children who do not seem to respond to physical punishment, in which case the adult needs to figure out another strategy than to make the physical punishment more severe. The latter course gets into child abuse rather quickly.