If other companies can satisfy the needs of the state, why not prisons? You wouldn't mandate that governments should build their own cars, for example?
In my opinion (and we can certainly debate this point) this should never be outsourced to third party entities. A rent-a-cop in a mall should not have the power to arrest customers (or even search their belongings) without calling the cops.
Outsourcing such functions have the inherent risk that the privat company cuts costs and corners and moreover hires unqualified and cheap staff, which makes a bad situation even worse.
Incarceration of a human being should never, ever be a license to aply additional torture in any way, shape or form. Private law enforcment with minimal oversight is a direct route to such excesses, which should not be tolerated by a civilized society.
You wouldn't mandate that governments should build their own cars, for example?
That's a rather silly analogy, don't you think? Consumer products usually don't violently intrude into the freedom and bodily integrity of other people.
[1] https://en.wikipedia.org/wiki/Monopoly_on_violence
edit : added link
There are, in my opinion, certain aspects of government, which never should be outsourced for private gain. A prison company being one of the most extreme examples.