Can I first say your question is an excellent one and I'm not sure I can answer it, however i wanted to share my thoughts.
In an ideal world society would not want people to go to prison because of of the cost to society. There are so many cost from physical, legal, emotional/behavior, health, recurrence, future generations and etc. So as a society we would want to avoid people going back to prison and we should support initiatives that lessen our incarceration rate. Now despite what some on reddit seem to feel no matter how much money you throw at this there will always be people you can't rehabilitate. But if we could rehabilitate lets say 10-20% more of people who would be repeat offenders how much would society save. Now the question we have there is would the people who enforce the law like that? If we have less crime that means less police, judges, DAs, jail guards, etc. I'm guessing they all want to keep their jobs so there is little incentive for them to change the system and if I have learned anything incentive is everything. They do have some incentive in the fact that they do want their communities to be safe and healthy.
However when you put in for-profit prisons you can take any incentive out of the picture. They get paid per inmate and often have agreements where their prisons stay at x% of capacity. They don't want to rehabilitate but actually have the opposite incentive which is to crate repeat offenders to keep their cash flow going.
So I'll say society/public prisons have some reasons to reduce prison populations and rehabilitate; private prisons have no such incentive and would actually prefer people to stay/return to prison.
Private prisons do not get paid per inmate, they get paid based on capacity. The "Kids for Cash" scandal was not about getting more inmates, it was about filling existing capacity and triggering the need for more private prisons.
