That doesn't help if the public doesn't care, and for decades there was no public pressure to reform any prison, public or private. Now that criminal justice reform is mainstream, private prisons have received a disproportionate amount of public attention, enough for the feds to phase them out. I hope the newfound criminal justice reformers don't declare victory as soon as private prisons are gone. Never forget that over-criminalization and mass incarceration preceded private prisons, not the other way around.
That's actually not generally true. It seems to me that If the government cares about prison abuse, it's relatively easier to make that a contracting criterion and switch contractors (or ban contractors) than to top-down reform an entire system that is run by the state.
I looked for but haven't seen any statistics, but I've heard of horror stories emanating from non-private state-run prisons just as from private prisons.
