There is a misconception about private property. People think they work and then the thing they have is private property for free. As if private property only has a physical manifestation in the form of a product. Private property is a physical object plus the services provided from the institution we call private property. This means that private property is protected by the judicial system. It is protected by the police. It is possibly protected by neighbours watching over the neighborhood. It's value may be a function of the value of adjacent property. If you consider unavoidable positive externalities as a positive aspect of private property, then those positive externalities are also a service provided by the private property instituion. In fact, governments build utilities and road networks, they protect the land through a military force. The government does a lot of things to make your land valuable. Then there is the community surrounding your property, the businesses providing jobs and shops selling products, your neighbors, etc.

When I think of private property I not only think of the object itself but also a stream of public services for which you barely even have to pay something. If you are a landowner you could now come up with the idea of selling the public services. The revenue that this process produces is called ground rent.

Is the market distorted by the landowner who is basically just selling free services from the government or is it the government that makes these blatant gifts paid for with taxes unrelated to land ownership?

Manipulation of rents will not reduce those public services, the value of the land remains.