We should zoom out in perspective. The question is not “is the experience in for-profit prisons better for incarcerated people”.
It is “for-profit prisons create a system with a financial incentive to increase the number of incarcerated people”.
For-profit is the delivery system, which should save taxpayer money. Systems where the institutions are directly administered by taxpayer funds and their attendant public employee unions also have political/financial incentives.
Tax funded prisons also have unions that vote for expanding prisons. The distinction doesn’t make much of a difference.