> We don't punish people because it makes us feel good or for some sense of fairness, we remove people for the good of society.

That might be true in Norway, but it's clearly not true in the U.S. U.S. prisons and prison policies are tacitly designed to make them as miserable as they can be without making it obvious that they are in fact torture chambers. The widespread use of solitary confinement alone, which is now clearly understood to be torture, falsifies your assertion. The death penalty too does nothing to advance public safety. It is vengeance, pure and simple (and very expensive vengeance at that).