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How much is land value, really?

A relevant query from Mohamad Tarifi showed up on the Facebook LVT group:

photo credit: Zoomar via flickr (cc)

A surprising lesson I learned from helping a family member shop for a house in the US: most property value is in the improvement (building) not the land. For example, in a 1M$ house only 100k-200k is land (and this is south california where land is supposed to be super expensive). Since I am new to all of this can someone please explain to me why this does not significantly weaken the LVT argument?
He doesn’t tell us which part of Southern California this is; nowadays there are plenty of places where land (and houses) are worth little.  But even in prosperous times, builders of new houses typically expect the land to cost maybe 20% of the selling price for a new house, so his figure is plausible for some areas. But a new house isn’t the average house.
Routinely, in any dynamic community, houses (as well as other buildings) are demolished from time to time so the land can be re-used. When this happens, it means the land with the house on it was worth less than the bare land.  The average house is somewhere along the path from “land value is 20% of total” to “land value is over 100% of total.”
The existing U S personal and corporate income tax cause an additional bias to underestimate land value.  The owner of “income property” can deduct an amount from her taxable income based on the “depreciation” of the improvement, but land cannot be depreciated.  And, since the U S Government has little idea what the selling price of land actually is, it is a simple matter for the “taxpayer” to overestimate the proportion of real estate purchase price which is for the improvement.