You may be confusing LVT with property transfer tax? LVT is a tax on ownership of land - driving down land value, not up.

In practice it disincentivises investment in land (rent-seeking and speculative land hoarding) while incentivising land development. In cities this manifests as more, cheaper, homes, and lower rents, and is highly progressive.

I say in practice because we have over a century of explicit and implicit LVT implementations in the real world to demonstrate this. Most implementations of LVT have gone down as described. Estonia is a pretty fantastic case study - 90% of property is owner-occupier! And you might find this new study of implicit LVT in the US interesting - LVT correlates with higher earnings and demographic diversity: https://www.sciencedirect.com/science/article/pii/S004727272...

The challenges for LVT are really about how to transition the tax in for areas that are occupied, but severely underdeveloped. If a low-density inner-city area ought to be high-density, the owners are being charged accordingly. Long term, it stimulates development and the new housing surplus (splitting the tax burden of LVT across a much greater number of owners) balances things out. But that's no consolation to the people being told they have to pay tax on their backyard as if it's already a block of flats.