Let's say someone has a house in a gentrifying area. The house isn't taxed but the land is, and property values are rising. Encouraging density means making it financially difficult for them to stay there, so they will sell to a developer. If the tax doesn't do that, LVT doesn't provide enough incentive to discourage speculation.
LVT advocates need to own up to what they're trying to do. There will be winners and losers. Someone with little income (retired) and property in a desirable location is going to lose.
And this is exactly the sort of thing that got Prop 13 passed in California. Homeowners really don't like it when their property tax goes up.