I disagree with the fundamental premise on both parts.
> "You didn't do anything to make that happen" is a useful generality and not a prescription of every single individual in the community.
In fact, everyone does contribute, positively or negatively, to their community. Either through involvement or absenteeism, or somewhere in between.
> Your fixation on this point reveals a very fundamental misunderstanding of the goal of an LVT
The goal is obvious and not a misunderstanding. The goal is a bad goal, precisely because it punishes positive involvement in the community. To improve the community means to increase your own cost of staying.
Imagine someone wants to avoid displacement due to their taxes increasing beyond their ability to pay. I don’t know why they would want to stay in their economically “inefficient” house, but perhaps it’s because home is where the heart is and they have sentimental attachment to their home.
If they want to keep your housing costs down, the best thing to do is poison the ground (metaphorically or literally) because it decreases the “productivity” of the land. Box stores in America famously pay low property taxes because building a box store actually decreases property values - they’re expensive to demolish and limited in utility, while being an eye sore that makes the neighborhood higher traffic and less undesirable. Mississippi as a state is cheap because the voters used the government to destroy public services - it’s in someone’s best interest to do this in a Georgism world if they don’t want to be regularly displaced.