hypercrites

We need a couple definitions: Public and monopoly.

Are public facilities only those wholly owned by taxpayers or is Applebee's for instance a public facility because they serve the public?

What is the criteria for determining whether something is a monopoly?  Market share?

Public would be owned by the public or tax payer.
In a case such as medical it would not eliminate institutions from entering the field as private. For example a publicly owned facility may have exceedingly long waiting time for non-essential services. Other private facilities could serve the very rich who are too good to be among commoners but they would have to bear the difference between the costs in a public hospital and the private institution.

The Dictionary.com definition of Monopoly serves well: "Exclusive control of a commodity or service in a particular market, or a control that makes possible the manipulation of prices."