It IS revenge. Institutionalized revenge. And there's nothing wrong with that.

Part of the social contract that any government with the governed, is to enforce society's laws by imposing punishment on those who break them. The type and severity of punishment must be a level that society sees as "justice". Too much or too little and it damages the legitimacy of government in the eyes of the governed.

It has far less to do with deterrence than it does with maintaining the social contract.

When that contract breaks, so does civilized society.