Anyone, residential or commercial, with a mortgage would simultaneously find a massive amount of their net value erased while stuck with huge monthly payments on top of massively increased tax bills, unable to sell assuming the higher taxes drive down property prices.
In a state with fully implemented LVT, you would expect most people in dense cities to be living in multilevel housing that makes more efficient use of land. Eg if your condo building has 5 floors, you're splitting your land tax 5 ways.
Sprawling single level houses would be a relative luxury.
It's not difficult conceptually to come up with schemes to tax wealth which doesn't unduly harm non-wealthy individuals (however you would define that level for these purposes). It's just that for one reason or another these schemes are not implemented, and one of those reasons is (plausibly) the political influence of wealthy individuals