The heck we do. Let a few thousand of them face the actual electric chair and watch the recidivism rates plummet. It's a real simple concept, actually. People hate to die. We fight it- spend countless millions of dollars in vitamins and potions and spas in an effort to avoid the final bell's tolling.
Crime rates are low in foreign countries.
In the Middle East, if you are caught stealing they cut off your hand. Maybe, but very effective. Japan also has swift punishment for criminals, as do other Asian nations. In tribal times, punishments were swift and brutal, yet usually fit the crimes they were intended to correct. American history shows a swift punishment meted out to all criminals.