Again, property tax is implemented by the assessment. Your example is a failure in assessing. It has nothing to do with LVT. Also, your desert example doesn't

Again, property tax is implemented by the assessment. Your example is a failure in assessing. It has nothing to do with LVT. Also, your desert example doesn't make sense. If the land is usable it will be taxed. If it is not usable it wouldn't be taxed heavily under the current scheme, nor would it be with LVT. I think you're underestimating how much people are already taxed for their property.