Well the private property rights you buy when you buy land include the state's ability to tax it. As for why it's an issue of distributive justice, that's simple. Ethically speaking, everyone has a right to use land, limited only by the equal rights of others. The rental value of land is the differential value of what one land plot can offer compared to what is available for free, aka "differential rent". That differential is a free gift of nature. As a matter of simple justice, paying those excluded from using land is the ethical position.

Meanwhile, taxing people's labor is a way of collectivizing people's labor, which violates the right to self-ownership.

As for the 'payment of services', this is simply a narrow view of the services land provides.

"The consumption tax that best fits Smith’s criteria is on that of spatial services. A tax on spatial services also best applies the Ramsey rule of taxing inelastic items. Space does not get used up, but space generates a flow of site services over time that do get used up, and is measured as the implicit market rent. For example, suppose the rental of a house includes a back yard. The yard offers a continuous flow of service as a place to enjoy the outdoors. The user consumes that flow over time. Though the space remains, every hour of yard service is an hour of spatial service that is gone as soon as that time passes. As a flow, the spatial service is simultaneously generated and consumed. It has been well known by economists since the classical economics of Ricardo that the taxation of land rent does not affect the economic rent. Since the supply of land, within some jurisdiction, is fixed, a tax on land rent does not alter the amount of land. Since a tenant does not care who gets the rent, the tax on land rent does not change the demand, i.e. the quantity of land demanded at various amounts of rent." https://sor.senate.ca.gov/sites/sor.senate.ca.gov/files/Fina...

Whether you personally use a service or not is irrelevant. If the land provides a service and you choose not to use that service, you are still depriving others from enjoying that service.

Amusingly, levying a land value tax alongside the Wright Irrigation Districts in California is what broke up the large landholders who were monopolizing access to water. This was widely viewed as an enormous success in policy, even as the large landholders screeched that it wasn't fair that they should have to pay for the water whether they were using it or not. https://www.henrygeorge.org/caldes.htm

A private lump sum payment is simply a private tax. How we treat land ownership is ultimately an ethical question, without the state your title to land means nothing.

"THE TREATMENT of rent as public revenue is part and parcel of an organic theory of the State.

In the contractual theory, government is a kind of business which extends services to landowners. They only need pay for benefits received, which are construed in the narrowest possible terms.

In the organic theory, landowners hold title to land as a privilege. In return, they owe the State - acting on behalf of the community - certain obligations. The entire value of land is regarded as a benefit received from government. This is in keeping with the definition of land as "Public Value" offered by Alfred Marshall, the distinguished Victorian economist.

Land and its value is the joint product of at least three things:

• nature, which created it;

• government, which acquired it from other sovereigns and protects it from other powers and extends public works for the public's benefit;
and

• synergism, which is the increment to value that spills over from social and economic activity in the neighborhood of each parcel of land. Value stemming from all these elements is regarded as unearned by the individual landowner. It is the product of outside forces and therefore a fit object of taxation."

https://masongaffney.org/publications/G44Philosophy_of_Publi...

You're welcome to believe otherwise of course, but trying to dispute the ethical position of land value taxation is like trying to argue against the laws of physics.