I would have assumed exactly the opposite in terms of urban land being uniform in value.
10 acres that are 30 minutes from Des Moines, IA are going to be very similar in value (price people are willing to pay) compared to 10 acres that are 10 miles down the road. Rural land is generally quite uniform and more likely to be functionally the same. In an urban area, say Los Angeles, 10 acres in Malibu (an area with very high demand for property) is going to have a totally different value (again, price people are willing to pay) as compared to 10 acres 10 miles away in skid row.
The problem, that other people have highlighted, is how do you (the government/IRS/agency in charge) determine the value of each of those land areas? Letting some city planners in LA decide that those two areas should have the same LVT, or allowing them to determine what tax each should have, is gifting a lot of power to people who may or may not be qualified, and may or may not experience any sort of consequence for poor decision making/ biased value assessment/ etc.
The exact way that sort of value/tax-setting would play out would be very interesting, but the unintended consequences could end up being pretty bad.
I've always thought it was interesting that property tax assessments don't just use the previous purchase price, and instead rely on a relatively arbitrary valuation. That could be one way to more accurately determine an LVT - make it a set percent of the previous purchase price of the land, that would allow the taxes to be priced in to land transactions.
I still just don't love the idea at its core.