Personally I don't want to live in a society in which homeownership is not possible. I could get behind an LVT on holiday homes, second parcels of land, etc. I wouldn't like it, but I can see why it may be needed.
But a primary residence being subject to an annual tax which can change and outstrip the ability of the owner to pay just means that there's no meaningful way to build stability. I think that's a pretty awful side effect of a flat LVT on everything; I'm invested in my neighbourhood and improving it based on the fact that it's actually mine for life (rather than being temporarily mine).
How stable should property ownership be in an area experiencing growth? I think this could be tunable with short term price increase caps that expire 5-10 years out, and reset when the property is sold or the owner starts paying the full market LVT again.