Alternately: Since natural resources are not created by people, there's no reason why a given person should have the right to profit from it to the exclusion of others. They didn't do anything to create the resource, it was there already.
The social value of private ownership isn't in permitting owners to profit, it's in aligning incentives so that a resource is put to the most productive use. Very often those willing to pay the most money are the ones with the most productive use, and so long as there's a private owner his interests are usually to sell to the highest bidder. More importantly, a private owner can't be corrupted into selling to lower bidders, whereas bureaucratic owners (public or private) can be.[1]
I [very briefly] researched Georgist taxation systems in the U.S. when taking a seminar on land use regulation. My tentative conclusion was that they weren't very effective because the bureaucratic systems for appraisal were very quickly corrupted--not to benefit individual politicians, but to satisfy the electorate, who often find such taxation schemes unfair.
[1] A private owner with multiple interests might be willing to sell one interest to a lower bidder in exchange for a higher bid for some other interest, though.
I agree with you that Georgism isn't perfect. However, I haven't seen a better solution.
You can't. No one person can. That's why centralized economic planning doesn't work. (I'm not trying to suggest that Georgism is centralized planning, or that Georgism doesn't appreciate the value and necessity of price signaling.) And private ownership doesn't necessarily lead to the most efficient allocation. But the point is that private ownership is a stable regime. There are an infinite number of regimes that would offer better allocation, but we haven't yet seemed to find one that is stable, or that we can make stable. (A big part of the problem, I suspect, is cultural, so I don't mean to suggest that Georgist systems are inherently unworkable, just evidently unworkable in recent American history. I think our social and political cultures play a big part in what make land value taxation seem unfair.)
That said, if the public believes land isn't being put to good use it can purchase the land at market price.[1] That still leaves accidental and speculation profits in private hands, but theoretically it puts a ceiling on inefficient allocation. Unfortunately, in some ways (particularly politically) eminent domain powers are at their nader in the U.S. Which is a big part of the reason why we can't accomplish things like California Highspeed Rail. I think that drives home the point that Georgist taxation is less workable today than it ever has been in recent history.
[1] That's required by law in some countries, like the U.S. In some other countries it's not technically required by law but it's often the case that the government does pay market price, simply because to do otherwise would seem unfair and lead to political backlash.
HSR would be easier with a land value tax - there would be a negative incentive to hoard land, so land acquisition costs would be minimised.
California is a great example: HSR battles and Prop 13 revenue dilemmas are things that land value taxes are directly intended to resolve in favor of the public wealth. But both of these phenomena have strong public support propping them up, directly and indirectly. Prop 13 was passed precisely because the public was concerned about the threat of people being priced out of their homes, and that sentiment is at least as strong today as it was back then. Land value taxes would systematize homeowners' worst fears, and they won't be placated by arguments or even evidence that shows that they're better off on average.
I'm tempted to say that people are just irrational or that the public often wants contradictory things, but that would be lazy--true but lazy. In any event, my point is that resolving these things requires more than simply engineering a system that works better on paper. Incentives have to be aligned not just in dollars, but also in votes; not just at the outset, but also on an ongoing basis. Georgist land value taxation schemes are fundamentally predicated on consistent, long-term application. Once exceptions are made it crumbles because not only do perceptions of unfairness increase, the utility of the regime declines. This is true of alot of things, even traditional land taxation, but it's especially true of land value taxes.
[1] Or at least I'll concede that point. It's not obvious to me if and how prospective public works projects would figure into land values under a Georgist system, especially in the rural areas where HSR battles seem to be the worst. (AFAIK, the more urban areas in and around Fresno were acquired and bulldozed rather quickly.) Particularly with land value taxation, the devil is in the details.
So profit that comes solely from owning a natural resource isn't earned; however, profit that comes from the labor of extracting the resource or from making something with the resource is.
However, under that definition there essentially is no such thing as "unimproved value"—unclaimed and unpreserved land would quickly become unusable for any purpose—and the proper LVT assessment in the vast majority of cases would be zero, or else so low as to not be worth collecting.