Presumably it would "save" you because your end tax would still be lower (as people whose multi-million dollar homes comprise only a fraction of their wealth would subsidize you). It's a bad idea for a bunch of other reason, though.

The "not saving" part is because if your house appreciates in taxable value - no matter, house tax or whole person worth tax - you have to pay more, and if all you have is the house itself (plus something which generated enough value to pay tax when house was cheaper) then your expense grows without your income. Even if you would comparatively pay less tax than your neighbor.