Prisons - If we assume the corporation profit comes from prisoner rent, the private corporation is incentivized to encourage more prisoners and longer sentences.
Im not convinced that is a healthy incentive, and the evidence seems to show it is not.
School privatization - Where does the profit come? if it is based on children/hour then the corporation is incentivized to have more people attending school for longer periods.
that again sounds like a problem to me - you COULD achieve it in positive ways, but you could also achieve it by not teaching anyone anything....or by teaching at a slower rate...
Hospital privatization - This just sounds like a total cluster fuck to me, assuming the corporation makes its profit from rent/medical treatment then the incentives are there to keep patients as long as possible and undergoing as much treatment as possible, while actually curing as few problem as possible...
Some things, are just not meant to be privatized IMO.