Earlier quoted context omitted.
This logic depends on law-breakers being fully rational agents. Yes, there are some, at least some of the time, but very few.
If they're not rational, they can go to jail? Isn't that the idea of jails: take people out of the system if they refuse to act by the rules of the system at other people's detriment.
To me, the length of sentences in the US suggest that a primary purpose is deterrence, not merely keeping dangerous people off the street.