Private prisons are largely a red herring. They account for some 8.4% of the prison population. [1] Many of the horror stories coming from them are simply from the fact that state corrections agencies willfully loosen their standards when contracting with private prison operators.

[1] http://www.bjs.gov/content/pub/pdf/p14.pdf, p. 14

Private prisons are more a symptom then a cause of high incarceration rates. States began using them in response to prison over-population - and the percentage of inmates in private prisons is relatively low (single digits IIRC).

edit: to be clear I am against privatization of prisons because I think the incentives are woefully misaligned, but wanted to point out it's inaccurate to suggest they're the cause of our high incarceration rate