Under the existing system you are incentivized for your own land to be zoned as highly as possible while your neighbors land is restricted as possible to keep supply low. Since everyone votes against you and you vote against everyone, zoning is low just about everywhere.
Under a land value tax this flips, and the majority vote would go to up-zoning.
And what is your take on when Minneapolis voted to allow multi-family units[0] and rents dropped[1] relative to other cities? Shouldn't those new units have brought higher land values, and with it higher rents?
If the land of Joe's neighbours has no restrictions at all, it will be valuable. But if Joe's land has a weird zoning that says 'can only be used by Joe' that land would be nearly worthless on the market, but good for Joe.
Less extreme, if you have a neighbourhood with plots that allow unlimited building and a few plots that only allow single family homes, the latter would be a lot cheaper.
Under a land value tax this flips, and the majority vote would go to up-zoning.