I agree you cannot predetermine the prison rate, but that also means you cannot look at the rate alone and determine that it is too high. It is complex.
Part of freedom is the freedom to make bad choices. One could argue that we have a higher incarceration rate because we have more freedom, for better and for worse.
I agree with those issues with for profit ran prisons as they are run today, without proper oversight and poor structure. But what if the profit incentive was changed? What if for profit prisons were incentivized to rehabilitate prisoners, rather than merely incarcerate them? What if they made their money based on how many of their prisoners increased their education levels, got jobs, and stayed out of prison? What if they could only be profitable if they actually did the right thing?
Government has done a really, really bad job at this. Government has prior to for profit prisons done most of the bad things you credit with for profit prisons in the prisons they run.
I think we can do better with our criminal justice system and our prison system, and with the proper funding and oversight, for profit can and should play a part. Our government is not good at DOING. Our government should focus on proper oversight and regulation.