The only right way to do private prisons is to give each prisoner a fixed grant with which they can use to buy space in a prison. This is the only way the prison's incentive can match those of the prisoner.
You get what you incentivize. If you incentivize headcount, you get a higher headcount (thanks to lobbyists) Your suggestion might improve facilities, but that's not quite the goal either.
If the goal of our system is to reform and reintegrate people who have committed crimes back into the society, maybe that's what we should be incentivizing.
We could develop quality measurements based on outcomes, and give bonuses based on the percentile prisons rank in.
