Er, an LVT doesn't tax the house at all, that's precisely the point. It only taxes the land... It's literally just a property tax that doesn't tax the house.
So if I've got 10 acres that I'm keeping as an undeveloped wilderness to provide habitat for migratory birds to use during migrations and you've got 10 acres next to mine with a 200 unit apartment building on it we pay the same amount of tax?
That doesn't seem fair since your 10 acres is using way more of nearly every government service property taxes fund and requires more of nearly every government infrastructure that property taxes pay for.
In that case, I'd imagine the solution would be to ask for a zoning change to the land (changing it's value), or put it in a non-profit which could have special tax treatment - or transfer ownership back to give under specific conditions.
That doesn't seem fair since your 10 acres is using way more of nearly every government service property taxes fund and requires more of nearly every government infrastructure that property taxes pay for.