Private prisons are a problem, but as other posters mention, a sub-double-digit percent of our prisoners are in them. One of the real problems, it seems to me, is that pesky little clause in the 13th amendment allowing slavery as punishment for crimes. The government leases out prisons full of people as a work force to private industry. There are many industries and companies in the US that are now dependent on what is essentially slave labor - and no, 16 cents an hour doesn't somehow morally absolve us of the problem.
I always felt that private prisons could work great, if specific incentive laws are passed. First, give the inmate a choice of which prison to attend, so they are competing against each other based on reputation. Second, if someone re-offends and ends back in prison, then the original prison housing them would be on the hook paying for their stay at the new prison. This gives private prisons an incentive to properly rehabilitate by making sure the prisoner comes out in a better situation than they went in (education, therapy, etc).
Yeah, they use the GEO facilities mainly for illegals now, because illegals have less ability to hold GEO accountable and navigate the overlycomplicated prison systems required to access your rights (and you must exhaust local administrative remedies through the Warden and then the BOP before you have access to the Courts). And that is considered progress in the eyes of the American system because it's all about appearances, not about actually following the Constitution.