As I understand it, property tax is simple when there's been a recent sale. The complexity comes from a similar issue to land value: no recent sale. In this case it's worse because valuing the land outside of what it's used for is a mess.

But this problem already exists. Many people live in homes for 30+ years and pay property tax on the land + improvement (physical home) value. Why would it be so much harder to hypothetically value the land without a recent sale (required for a LVT) than to hypothetically value the land + improvements without a recent sale (required for property taxes which currently exist in almost every city in America)?

Because their neighbours have sold their houses recently. So using similar sales as a baseline and then factoring in a few differences between those properties and the one that is being assessed is much easier than doing that and then subtracting the built-up value.

Basically all of your data points are the built-up prices. So it is going to be easier to estimate the built-up value than the raw property value. Maybe not much easier, but definitely not harder.

Then yes, I’ll agree with that. Both can be difficult but valuing just the underlying land is harder.

Do you think taxing by sub components of land would be simpler yet? Maybe we should tax by rock content.

Or maybe a tax based on more things has nothing to do with complexity. The largest market is for land and structures. That makes it the simplest to value.

There's not an argument from economic efficiency to tax by rock content.