if you add prison guards unions - which are formally non-profit, and that only means that they have no taxes to pay and they have nobody else to give the formal profit away, and as result they have all the money they collect to themselves - you'd get pretty much 100% of US prisons run by organizations with direct financial interests in growing the prisons in size and number.
yep, there is a reason why military for example aren't allowed to form a union. I hope CIA/FBI/NSA aren't allowed to have it too. And prison guards and police shouldn't be allowed to. Holders of "license for violence" shouldn't have masters other than the government hierarchy they belong to thus minimizing conflict of interests.
Citation for the "Many"?
Only about 5% of prisoners are in private prisons.