Three things that should always be ran by government: healthcare, education and prisons.
They must exist, and privately owned ones will always have wrong base incentive.
With prisons especially, it is not the interest of private to rehabilitate, but to get people in prison loop. It just cannot work. It is just easy to sell to people because people want prison to be punishment facility.
Critical infrastructure (water/electricity/internet) are of course things were government needs to be atleast heavily involved and controlling. And predatorial industries like gambling should be controlled.