> LVT would push up the supply of rental properties by ensuring that property owners who don't rent out their properties or who don't make efficient use of land lose money.

That doesn't follow. If LVT reduces the net return on rentals, it will disincentivize construction and maintenance of housing in the first place. If it creates a net negative or zero return on property ownership, it may lead to abandoned/undeveloped property instead of housing development, or more property being used for other purposes than housing.

It's also worth pointing out that the existing ad valorem tax system used for property taxes is functionally equivalent to LVT, and does have these influences on the housing market. LVT proposals are distinguished by their being rooted in (fundamentally flawed) Georgist theory, not by being unique as a form of taxation in practice.