Inaccuracy isn't a very big component of this; assessing the value of land and structures isn't perfect but there's no obvious reason to think we're way better at one or the other. The point of this is that taxing the land only would lead to land being used differently, which would benefit society.
Suppose there is a plot of land which (from some omniscient point of view) would offer maximal benefit to society if a four-plex were developed on it. The point of a LVT is that, under a LVT, a four-plex would be developed on it, not because anyone forces it but just because that's what's in the landowner's best interest; whereas under the current system (in which the structure is also taxed) the landowner might find it more profitable to build a duplex instead. The deadweight loss is the loss to society when the landowner builds something that's in their best interests but not society's.
That's hard to prove for any specific piece of land, since we don't know what the omniscient-view "right" use of the land is. But if you accept the idea that there is an optimal use, and you you trust the whole idea of free market price discovery, it's reasonable.
Inaccuracy in the end is a HUGE component of this. If you can't have an accurate value for the land, the long-run incentives converge to a system where the land value assessors have a lot of power, and could use that power to screw you over.
> but there's no obvious reason to think we're way better at one or the other.
There’s a very good reason. Sales of buildings plus land happen all the time, whereas sales of just land are virtually non-existent in a lot of the places with the most valuable property (e.g. Manhattan). Without real sales to tether the analysis you are just guessing.
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.
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).
Suppose there is a plot of land which (from some omniscient point of view) would offer maximal benefit to society if a four-plex were developed on it. The point of a LVT is that, under a LVT, a four-plex would be developed on it, not because anyone forces it but just because that's what's in the landowner's best interest; whereas under the current system (in which the structure is also taxed) the landowner might find it more profitable to build a duplex instead. The deadweight loss is the loss to society when the landowner builds something that's in their best interests but not society's.
That's hard to prove for any specific piece of land, since we don't know what the omniscient-view "right" use of the land is. But if you accept the idea that there is an optimal use, and you you trust the whole idea of free market price discovery, it's reasonable.