The US prison system has many issues, but the attention given to private prisons is extremely myopic and scapegoaty given that they account for less than 10% of the US prison population.
Alternatively, one could consider "private prisons" to be a symptom or symbol of a problem that is well understood to go beyond prisons that are 100% private. What about contractors, either for construction or operations? What about the people and companies who benefit from prison labor? What about the lawyers and others who make their money by helping to move people in and out of a too-large prison system? They're all part of an overly privatized prison system, even if they're not "private prisons" in the strictest sense. "Private prisons" is often intentional shorthand for the broader problem of imprisonment for profit, because it's easier to say. I doubt you'd find many people who are bothered by private prisons who are totally indifferent to all the rest. "Less than 10%" seems a bit myopic to me, in the sense of representing too narrow a focus on one factoid.
Yet account for a disproportionate amount of lobbying, which is what this article and discussion is about. They're literally helping to write laws to increase the overall prison population (public and private), which is a problem for a society with an already very dysfunctional criminal justice system.