The government has a financial motive, on behalf of its citizens, to avoid unnecessarily imprisoning people. Private prisons have a financial motive, on behalf of their investors, to imprison as many people as possible. This means that there is an inherent, and fundamental conflict of interests between the citizens, and the owners, and investors of private prisons.
The only way to reasonably prevent this conflict from causing unnecessary damage is to make private prisons illegal, or severely restrict their lobbying to prevent them from fighting the financial motives of the citizens in their own government.