Good riddance. The whole premise of private, for-profit, prisons has always seemed deeply troubling to me. The focus of a healthy prison system should be to rehabilitate people and help them turn their lives around so that they contribute positively to society. That can take years of hard work by the individual, and require assistance from professionals (therapists, teachers, ...). A for-profit company by definition…
I would recommend you do some research on this topic. Your giving talking points produced by mainstream talking heads. When in fact, research points to private prisons being better at dropping incarceration rates through the programs offered at them. Therefore increasing ones chance at correct rehabilitation. https://www.researchgate.net/publication/249718665_A_Compara...
I don't think it's valid to draw concrete conclusions about the current crisis from the study you linked. There are far more variables at play than were studied in the paper, and those variables - such as racism, increasing societal inequality, etc - matter.
Also, reasons cited in that paper for the reduced recidivism are to do with the programs offered by the private prison. Are private prisons in all states / California allowed or incentived to offer similar programs? Do they choose not to?
These things affect the statistics, and drawing strong conclusions from that paper about private prisons in California today may lead you to invalid conclusions.