I don't think that this is a correct model of how a high LVT would work. But more importantly, let's say it did- now you don't get any of the supposed 'efficiency' gains.
I think LVTs are a great idea for a brand new society, and they certainly would work- by making land too valuable for SFHs, so that it has to be used for its highest & best usage. But if you're not forcing homeowners to do that, you're not capturing any of the efficiency gains, so LVT just becomes another tax. It's either forcing landowners to develop apartment buildings on valuable land or it isn't- you have to pick one