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The fundamental assumption of LVT is that society should be the owner of the land - i.e. that the land is commons. Government can be a manager of that land, but it only has such powers because the shareholders (everyone) vest that power in it.

The basis for this assertion is that land supply is fundamentally very scarce, so this is zero-sum game. If some have too much, others have little, and the former can extract substantial economic rent from the latter.

Nevada for a short time had the option of getting allodial title.

https://en.wikipedia.org/wiki/Allodial_title#Nevada

Proper use of allodial title and homeowner's exemptions could go a long way.

I had never heard of this, super interesting, thanks.

"ultimate owner" is too broad a brush. Long and detailed debates went on for generations over this. The origin of the USA is in the right of States to determine quite a lot of the details. Federal taxation is only a hundred years old here. Texas and the mid-west are different than California which is different than Florida.