Private prisons are a red herring. The vast majority of prisoners are not in private prisons, and states have been moving to get rid of them. In many big states, like New York and Illinois, private prisons weren’t legal to begin with. Rikers, the NYC jail famous for its abuses, was public.
People make private prisons to face of prison abuse for tactical reasons. In reality, the story of the American prison system is the story of the government: voters who demanded “tough on crime” laws; brutal publicly run police; harsh publicly operated prisons; all tied together and supported by public unions.