Of course, you could alternately just sell your now-valuable land. However, the higher the ongoing tax bill (due to the LVT) the less people will want to pay for your land. The LVT captures some or much of the value currently accruing to landlords (depending on how high it is).

High property taxes can serve a similar function. Taxing the unimproved value of the land removes a disincentive to improve the land, though. If you knock down your house and build a much better one on the same land, your property taxes would go up while LVT would not.

LVT vs property tax is not the main point, though, in my opinion. The real issue is moving from heavy reliance on income tax to heavy reliance on property tax or LVT.

Granted, any LVT won't approach the 100%-of-rents rate, so it's a proportional thing.

>for the purpose of encouraging building housing how is a land value tax functionally different from a property tax?

A land-value tax is indifferent towards a single-family home and a thirty-story apartment building on identical plots of land. Property taxes aren't, they add an additional penalty on the highly-developed land.