A real issue IS who owns or manages the prisons. If the profit motive is what drives prison expansion, then society will experience a form of regulatory capture in hyperacceleration.
Many of those programs and processes are being taken over by private entities. You are no long just paying out to your municipality, county, state or country. You're paying out to them and the private company who demands your payment or you go to back to prison for non-payment. They still profit and your debt racks up.
You are paying out fees to the private company for your detention, your lodging, your processing and probation on top of what the state is paying them to hold you. If you cannot pay them back, you are free to spend a day in jail for each $10-$40 of your debt owed to your captors. They get to collect from the state as well.
Then, with the money they've been collecting, the private entities go and lobby to make sure there is a steady stream of constant offenders to keep profits increasing every quarter.
Sometimes it makes sense to bribe judges to send innocent children to your private juvenile detention center to collect those fat state grants, a la Cash for Kids.
The profit motive perverts justice and seeks to turn everyone into customers of the private justice system.