Land value *is* currently taxed.

Yes, this is a common misunderstanding. The problem is that land is typically taxed at the same rate as improvements, and that this tax (~1% in US) is well below land rents. Some cities like Harrisburg, PA have split-rate taxation, where land is taxed more than improvements. This would be a good direction.

I have never seen a situation where an unimproved property’s value went up and the corresponding tax on that property didn’t go up with it.

Laws like California’s Prop 13 limit the annual increase on property taxes, so taxes don’t respond to true appreciation of the asset.