It's far from as simplistic as you portray it. Voters demand "truth in sentencing", in other words longer sentences and less parole, but then balk at the cost of public prisons. Legislatures are sold on privatization as a cheap alternative, but don't consider that as a rule you get what you pay for.

Republicans in general tend to see privatization as superior to the civil service on philosophical grounds; they believe the private sector does everything better and cheaper than government can, despite past experience.

Michigan has not had private prisons for 20 years now, but the Republicans in our legislature keep trying to bring in bills to "study" what it would cost to turn over one or two facilities as a "test case" to private industry- even though we did it before and it was a failure.