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
Nimbyism would become even more extreme.
You're gonna fight hard against your neighbor adding a Duplex, triplex, fourplex, etc. because with an LVT your taxes very likely go up as a result.
Imagine the uproar when a developer comes in and converts some of the SFHs next to granny's house into a 4-plex and now granny's social security doesn't cover her taxes and she has to move to the old folks home. Sure she can theoretically take out a mortgage or second mortgage against the theoretical increased land value but now you're forcing granny into debt.
How are you proposing to calculate land value?