And the way to keep this reasonably neutral (ie not dump a massive tax out of nowhere on people), is that LVT replaces at least a portion of say, income tax. That makes it politically viable as well.

I would imagine this would have a weird effect on land values if enacted. People couldn't afford such a large tax, so prices would generally go down. Since the value of the structure won't go down (because that's based upon cost to build) loss of value would 100% go to the land, which would lower the LVT. But the price to rent wouldn't necessarily go down, since the total ownership cost wouldn't go down.

It obviously would hit an equilibrium at some point but I'm not sure where.

A secondary point of something like an LVT is to encourage density, since you get %0 taxation on the building itself, so it can afford to be more expensive. What uses less land, less energy and requires less miles of pipe, wiring and roads to service? A high rise with mass transit train service. A 50 story building on the same size of land next door to a 5 story building will have an approx 10x overall lower tax rate per sqft.

Land developers and people would naturally become economically incentivized to live in apartments as a result, unless they live somewhere somewhat rural already.