Isn't the primary issue anyone has with private prisons the same one we have with defense contractors: that they might, would, or do subvert the system to get innocent people imprisoned or their prison terms extended in the case of private prisons, or promote wars America doesn't want or need in the case of defense contractors?
What I mean is nobody really cares if prisons buy commercial toilet paper, for example. (As opposed to a hypothetical government toilet paper.) Nobody cares if the military uses the private industry for procurement of computers or whatever. We don't feel the government should be creating its own version of all private industry products.
But when the prison itself is private - and likewise when defense contractors themselves are developing, shopping around, and selling new weapons only to the military, that the military didn't ask for - then suddenly there is a new player in the budgeting process.
Ideally few or no people are committing crimes. If the prisons have excess capacity, free beds - good! But if it's a private prison, how can they fill those beds? Well, by working to imprison more people.
This is the incentive structure that people don't like about private prison.
In the United States it's de facto "illegal" to walk around while being black: there is a high chance you will eventually be jailed on non-existent charges. (And accept a plea bargain, for example, rather than risk a really long term.) I'm a white guy. If I had lived the exact, exact same life, done every single action exactly the same (and this is true of other people reading Hacker News) I likely could have been jailed for no reason at all, just for walking around while being black. That's a fact. I probably would accept the plea bargain I'm offered, too, and resolve to work for change later. What am I going to do? Tell the judge and prosecutor (who often is scored based on how often he gets a conviction/plea) that he and the system are racist? How well will that go over? Will it get me my freedom? Or will it get a vindictive term from the judge. I'd rather just sit in prison for a few months and then avoid the cops better next time, I think I would decide. (Rather than risk a 20 year prison sentence, again, totally innocent of anything. A few months' plea - which my counsel would probably advise I take - is nothing compared to that.)
So why are innocent black people jailed? Well, to fill prison beds, apparently. That is one of the reasons that people don't like private prisons.
We don't want anybody to be "selling" prison, so we don't want prison to be a private enterprise. It's quite straightforward and is something most people understand very easily.