Yeah and the Fed isn't a private entity. Look you might split hairs all you want but if it quacks like a duck; the fact is that everything you mentioned is proof that some prisons are private in all but name. Specially when the state allows them to run like for profit enterprises and has a vested interested in generating more convictions.
That makes no sense. How can more convictions be up to the private entity? They play no part in criminal justice system, just corrections. And since the rules and regulations that are followed are the same as if the State DoC were running it the only real difference is where the prison staffs' paychecks are coming from. Governments contract work all the time.
So you think that arrest quotas and state legislation that allows harassment by the police is completely unrelated to governors receiving payment from said private entities?
Could be truth but then:
"Last year, the company made an offer to 48 governors to buy and operate their state-funded prisons. But what made CCA’s pitch to those governors so audacious and shocking was that it included a so-called occupancy requirement, a clause demanding the state keep those newly privatized prisons at least 90 percent full at all times, regardless of whether crime was rising or falling.."
Link to article
https://www.motherjones.com/crime-justice/2013/09/private-prisons-occupancy-quota-cca-crime/