The max that can be paid out in an insurance claim is the buildings value. This is less clear cut. A business could self insure for a portion, or all, of its insurance and then understate the buildings value.
One problem is that with high land value taxes, the property value would be equal to the buildings value, since the land tax would eliminate the value of the underlying property.
With high land value taxes, the usage value of the property will not go away. The big city central district will still be a place where businesses and people will want to be in. All that changes is to whom the rent goes to. Right now it goes to the banks in the form of interest for home/commercial loans. In a world with bitcoin and land taxes, it will go to the local government.
On second thoughts, for minimum tax, you want to overstate the buildings value. Self insuring would just push down the effective buildings value, so that would make the tax worse.
So, your idea is that if someone is willing to insure the buildings for $X, then it is assumed that the building is worth $X?
Side payments to the insurance company could distort this. If there is a 1% chance of the insured thing happening, then businesses might be willing to insure for a higher than stated value plus some kind of commission. This is balanced by the fact that insuring a property for more than it is worth is extremely risky. It creates an incentive for the owner to have an "accident".
There could be a law that intentional destruction of your property to claim the valuation insurance is legal. Lying to the valuation company would be grounds for being sued though.
I still think some kind of averaging would be a good idea. For zero distortions, nothing the property owner can do should be able to change the tax they pay.
In theory, the government could burn down the building and pay the stated building's value if they think you have over stated the building's value.
Land generally is worth more to the current owner than to anyone else, so the value an owner places on his land is likely to be higher than market value. Land with high sentimental value would end up being taxed more.
Finally, it is more important that the assessed land value is defined by a clear rule than having extreme accuracy. Even if the assessed value was 50% higher than the actual land value, then the tax would still have zero distortions. The only time there is a problem is when the assessed land value is larger than total property value. Setting land value = (total property value) - (insured building's value) guarantees that the assessed land value is less than the total property value.
In theory, it is possible to have a negative buildings value. This would be property where the buildings are actually dis-improvements. For example, a nuclear waste storage facility could very easily have a negative improvements value.
