Sure but when neighbors improving the land next to you results in your tax rate increasing significantly people obviously tend to be against that.
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.
You pay tax based on unimproved land value so what your neighbor builds doesn't matter. In your scenario, for what you're talking about to happen, everyone in the neighborhood needs to be building fourplexes and opening local businesses which would change the makeup of the entire neighborhood and taxes would adjust accordingly. So no, your neighbor building a duplex doesn't spike grandmas taxes. Under the current system, grandmas neighbor building a fourplex can increase her property value and have her paying a higher property tax anyway.
How are you proposing to calculate land value?