A land value tax would fix this
Changing the tax structure doesn't remove that restriction.
On the other hand, once you remove the zoning restrictions, the existing economic incentives will produce densification without LVT, tbat's the whole thing the zoning restrictions exist to stop.
That is an irrelevant counterargument, since the idea of dense housing leans towards tall apartment buildings, not trailers. No one should have to live in a trailer.
The township of the Fairhope Single-Tax Corporation near Mobile, Alabama was originally conceived as an artist's colony but is now occupied by families with a median income of $95K. Density is almost exactly 1 housing unit per residential acre. The feds have built 140 Section 8 subsidized units, but there do not seem to be any privately built high density tall apartment buildings of the type you want to see.
Can you point to an LVT place in the US where developers have chosen to build large numbers of actual NON-LUXURY high rise apartment buildings for the benefit of non-rich people? That would be a big newsworthy success story if it actually happened.
There are developers that make their money building high rise apartment blocks. Are any of them lobbying for an LVT so they can build more low cost housing?
There exist plenty of old buildings in urban centers that meet this criteria. There is nothing in principle that is stopping their construction. It's in the same imaginary league as LVT for that matter, meaning that if one can manifest, so can the other.
Luxury buildings are made because of a profit motivation. Even so, once the supply is increased by 10x or 20x, their prices too will come down. China is a supreme example of having cheap apartments.