This 100%. Private prisons are used to create a contrast statement for corporate suppliers of prisons and lobbyists to "show" how cheaply operations can be done. They are a conference booth to lure states in regarding shredding prisoner QOL for a 6% revenue increase can work without increasing the inmate death rate too much.
The Industrial private prison complex owner group don't want to operate, they want to sell support, training, equipment and materials to public prisons not operate (like a defense contractor), because a prison is very complicated management problem and has little public reward over budget efficiency sadly (things are changing but slowly).