It's actually because public policy is engineered to send as many poor people towards prisons as possible due to the private prison industry doing HEAVY political lobbying in the area. Especially the precedent of sending mentally ill people to prisons rather than institutions as a cost-saving measure.
A high incarceration rate doesn't mean we have better police, it means the bar for an 'imprisonable offense' has lowered, likely in tandem with the rising profits of a privatized prison industry. It also means that non-violent offenders are being given increasingly length sentences (see: mandatory minimums) as a method of funneling new meat into the prison factory. Here's something interesting: when determining parole (supervised release from prison), courts use testimony from officers and administrators at the prison regarding the inmate's behavior. This makes sense, until you realize that the prisons themselves~~the officers, administrators, and sadly, lobbyists~~benefit directly from keeping that jail at MAX capacity. They are being asked to willingly give up a small source of income, and subconsciously or overtly, provide more critical testimony of the client to ensure they remain in prison. This is why statistics show a significantly lower chance of parole from a private prison than a state-run prison.
Remember that "private prisons" aren't saving money, they're saving time and effort. The government still pays the guards, cafeteria workers, and administrators through stipends provided on a per-inmate basis. This means the full cost of the prison--and more, like lobbying and research costs--are coming from the public dollar. You are literally paying to be kept as a slave.