I don't think this is why it won't get passed on. In theory the lowest income could leave the state and higher income renters would come in.

But in reality a land value tax incentivizes higher density housing. A single house and an apartment complex pay the exact same amount of tax, while the apartment building can split it up over many occupants. Land value taxes are a very natural hands off way of encouraging the right use of land, empty lots and car parks become unaffordable in highly desirable areas while apartments become relatively very cheap.

In theory the land value tax could be set so the overall taxation is the same as before, but but the distribution is such that the people with massive blocks of land in highly desirable areas foot most of the bill. This would over time make housing cheaper over time as more housing is built to reduce the tax burden.