Land value taxes aren't about destroying natural land to extract value.
The point of taxing the value of the land in urban areas is that a lot of the time places essentially squat on land that could be better used. A car wash building will have a low assessed value for its improvements compared to a biotech building. For example, in my city we have a carwash with its improvements valued at $400,000 and a biotech building with its improvements valued at $275,000,000. The biotech building uses only double the land, but pays a ton more taxes.
In my city, there are lots where they're basically abandoned. The owners know that they can just sit on the land and it'll increase in value over time even if it isn't used for a productive purpose. During this time, people need housing, businesses need office space, etc. This isn't "natural land", they're gravel pits.
In fact, lack of a land value tax causes us to destroy natural land. Instead of using land well, we sprawl and pave our way into the suburbs and beyond.
Not all land is equally valuable and land can be made non-valuable from the standpoint of a land value tax like parks and nature reserves. A land value tax isn't really meaningful in rural areas where the land isn't really that valuable due to its location. Where a land value tax is meaningful is in cities where land is scarce and we want to put it to good use.
In a city, we don't want someone keeping an empty lot for decades so they can become richer based off the hard work of others around them - productive investors creating housing and office space, workers and artists making an area more desirable, etc. They sit on their empty lot paying nothing in taxes while others make them richer. A land value tax says: put that land to good use or your investment won't pay off that well. Under the current system based on improvements, they pay almost nothing and leech off the hard work of everyone else.
Land value taxes don't destroy natural land. They'd probably preserve it. A land value tax might destroy surface parking lots in dense cities, but that isn't "natural land". They're a poor use of space. I live in one of the densest cities in the US and around the corner from a lot of 1-story retail. It would be better for the community if that retail had housing on top and a land value tax would encourage that.
The alternative to encouraging good land use is having sprawl. Sprawl doesn't preserve natural land, it destroys it. It also destroys our climate with the carbon emissions from people who then drive everywhere.
A land value tax isn't about taxing all land equally across the US. If you have land in an area where land is plentiful, then it doesn't have a high value (because it's plentiful) and it doesn't need to have a lot of value extracted from it. If you buy land in Manhattan, Boston, etc. and decide that you like it as an abandoned piece of property, that's not good for the community and there should be pressure on you to put it to better use or sell it to someone who will put it to good use. A land value tax is about taxing land in a way that prevents someone profiting off squatting on land.