a) You're implying that we use sale prices to set the assessed value of property today; I believe that's often not true. I happen to have the tax slip for a property in front of me, the assessed value is about 80% of what I paid for it five years ago. Assessments are already inaccurate, because they're more a product of politics than science; a LVT wouldn't magically fix that, but AFAICS it wouldn't necessarily make it worse.

b) You may not be confident in your ability to distinguish the value of the land from the value of the structure, but your insurer is. If you want to know e.g. how much your home's value would improve if you finished out the basement or built a garage, they will go through it with you on the phone. Sure, it's something of a guess, but a very educated one.

Buildings are demolished in Manhattan on a regular basis, granted not that often. There are real sales of empty plots.

Also if you know a building would cost $X to replace, but the plot with it sells for $X+$Y, you have some real information, not just guesses!

How much would it cost to replace the Empire State Building?

I don't know. I do know that 99 Church Street sold for $170 million, and was demolished, so that that figure is the land price (before adding back the cost of demolition).