> A land value tax taxes the land such that the market cost of the home is equal to the cost to build the housing on top of the unit.
To do that, an LVT would have to be calibrated so that it was enough to bring the market price of unimproved land to zero, plus (or minus, in certain market conditions) an additional amount needed compensate for dynamic supply and demand effects (lots of people wanting to move in plus building lag driving prices up above expected long-term equilibrium, lots of people moving out doing the opposite.)
> The land tax will put the land to best use,
Perhaps, but if so...
> and that will drive up the supply of housing units
...then not if housing units aren't the most profitable use of land in the local area it won't.
> All of this while the average person sees lower tax rates
Confiscatory (and the level of LVT you suggest is exactly that) taxes on land don't reduce tax rates for the average person in a country with a nearly 65% pre-policy homeownership rate.
> The money available to collect from NYC and SF land taxes alone could fund a nation-wide UBI.
No, even if that were true pre-policy it couldn't after you enacted it, because you are ignoring dynamic effects. Confiscatory taxation on land will catastrophically drive down land value.