Private prison contracts are structured to basically provide taxpayer-subsidized slave labor.[1][2] It is just another Reagan-Thatcher era privatization scam.
At some point blaming administrations 30 years ago for practices continued by subsequent administrations becomes deeply dishonest.
California for instance (referenced multiple times here) has had many governors since the Reagan days and could have ended the practice on a state level, and at a federal level the pendulum has swung to both sides on multiple occasions. Any of these administrations could have made it a priority, but did not.
[1] http://www.motherjones.com/crime-justice/2013/09/private-pri...
[2] http://www.motherjones.com/crime-justice/2015/06/private-pri...