You are incorrect about poor people not paying the tax. They live somewhere, even if that somewhere is owned by another person. For example, if you are renting, your rent payment is covering the tax for the owner.

That $15-60k per month might add up over time, but I doubt it would do anything to fix inequality, especially since it is regressive and applies to everyone. People with sizable properties who are paying that much probably have access to a resource which they sell, like grazing, oil, or water. The normal people paying the tax at $3-10k per year (possibly through rent payments) are going to see it add up too, probably in a more impactful way. I say this because it will impact their ability to raise and preserve capital, especially since they implicitly own less capital in real estate and wouldn't have access to resources to lease. The only benefit is that you could game the system and live in a tiny property to avoid paying much tax while making a lot of money, but that's only a couple percent difference in the states that have income taxes anyways.