I get your point, but it still doesn't change the overall outlook of your prison system.
E.g. corporations making dirty money out of providing crappy meals to inmates, etc.
Mind me, my country's prison system has similar types of corruption -- but it is mostly a matter of managers hiding supplies... because if jail police, janitors, and managers are state jobs, nobody is getting paid "more" just because you get more inmates. In a 100% public jail system, more inmates = more work.