The same entity (government, state or federal) that sentences individuals to imprisonment should be the same entity responsible for bearing the burden of imprisoning the individual.
My big complaint with private prisons, as they stand today, is that they tend to get paid based on heads and beds. As such, prisons are rewarded when prisoners behave badly (extending their stay), and when former prisoners reoffend (repeating their stay). There are no countervailing economic pressures.
If we want prisons to work, we need the economics to work in favor of societal goals. Everything else equal, a prison that generates low recidivism should get paid more than one that generates high recidivism, because they're eliminating future costs.
This is true, but we already ignore that for our prison population. Otherwise, our system would be less punitive and more aimed to reformation and building productive citizens.
Inmates sometimes end up staying prison longer than their original sentence because of crimes they commit in prison. The point I was making is that a private prison warden has much more of an incentive to punish those crimes severely than a public one does.