For real estate, at the optimum land rent, land would exchange hands at a value of roughly $0 (structures on top of the land would modify the total property value). Given the high transaction costs of land, and of changing ownership, there are other forces that shift the true land price away from $0 under a full LVT.

There would need to be exemptions or other ameliorating of the coercive effects of full-land-rent LVT for those living in a primary residence. Nobody wants to force grannies out of their homes, for example. But the coercive effect of land taxation would otherwise mean that land would be used far more productively, with more stable prices and above all more affordable prices. It would also require getting rid of density restrictions that are not based in actual health and safety (ie pretty much all of them). But even somewhat small changes in density can open up massively more land for use.

It doesn't take many homeowners to completely shut off the market for land and corner it all. Not many people watch zoning boards, and fewer pay attention to how limited land use is, and even fewer who are in power do not directly benefit by the massive bubble on land prices.

And we really do have a massive bubble on land prices due to rentierism. So any sane deflation is going to require a gradual phase-in of an LVT, with probably 2+ decades of gentle deflation of land prices. And as soon as that starts in, there are the makings of a tax revolt. In California, we have been suffering from the tax revolt of Prop 13 for 50 years, and we are barely seeing any cracks in the army of anti-tax Prop 13 supporters.

So the politics of a full LVT are extreme, especially in a land where every middle class person is supposed to own a bit of land and defend it like a castle, and often when that defense means stopping any change. A full-on LVT is meant precisely to stop land hoarding, so as long as a majority of people see that land is theirs' to hoard, it's unlikely that an LVT will be passed. Unless imposed from in high by a technocratic elite that's trying to maximize social benefit, rather than individuals looking only to maximize their sole benefit.