Judicial corporal punishment doesn't fit with American society at all. It's just not in our culture. We view a government that can punish prisoners in this way as tyrannical, and put in the 8th amendment to protect us from such punishment.
As someone who is trained to be an educator, I am not trained to administer corporal punishment, nor would I want to be. Since its purpose is fear, that also goes contrary to the educational process and distracts students from why they are there. Plus, how would that function in today's lawsuit-happy society, where grabbing a student's arm can be cause for dismissal of the teacher?
Any number of parenting studies suggest that any control or conditioning achieved with kids through corporal punishment can also be achieved in other ways, and usually more effectively.