I'm late to this, but I wonder if Charles' analysis ought to extend beyond private prisons to address all the ways in which prisons and jails have come to privatize essential services. This includes telephone calls and digital communication, which are largely controlled by a legal monopoly, along with medical treatment and food preparation.
The hyperlinked stories and legal cases are but a few examples of the potentially life-altering negative outcomes that have come out of privatization. One of the major challenges with combating this trend is that documenting wrongdoing and amassing evidence necessary to prepare conditions of confinement claims is extremely, extremely hard (and expensive, for a population that is perhaps the most economically disenfranchised of any in the U.S).
But we have seen that organized social movements have won victories and that zealous legal advocacy can unwind some of the worst consequences of mass incarceration. EA organizations are already supporting organizations doing this work, like Prison Policy Initiative (an Open Philanthropy recipient). But because of how localized punishment is and how limited resources remain, there is far more that could be done.