For Profit Prison Systems benefit no one except those that own them. Many times there are instances where there is inhumane treatment of prisoners and an increasing number of people going to jail over the smallest offences all because the owners of these imprisonment systems want to continue to rake in money while innocent lives are destroyed and those who are capable of rehabilitation are left to rot, forgotten by the system.
While this question calls for a more in-depth debate, there is no question that many of these services were not available to prisoners prior to out sourcing them.
I, personally, believe there were humans in prison that suffered tremendously from neglect of all kinds and health care would be premium. As Americans believe that even those convicted and sentenced to prison are not meant to suffer from neglect and so these services are a great benefit to reforming prisoners so they can be released back into society.
For profit prisons are not the answer for all the cost overruns and mismanagement problems with public prisons. However, properly ran they can be a solution to some of the mismanagement and cost overruns inherent in public prisons. Public prisons have a number of problems that are present in many publicly operated bureaucracies. One way to encourage the public prisons to operate better is to have have a private jail option available.
I don't see the benefit in changing the arrangement the government has right now. A lot of work is contracted out by the government to "for profit" companies.
It's not like a lot of money would be saved and sometimes private companies to a better job because they have an investment in their business.