Yeah, you could do that.

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).