If you add up the value of all the land, how does it compare to the budget of the government.

If the budget is, say, 100% of the value of the land, you're stuffed? I mean, obviously you can set a tax rate as multiples of value but land almost immediately becomes worthless and all multiples of 0 are 0.

Where would all the people go to live, out to the ocean?

I only give away the land, not the property on it. I assume in the real world we'd get some financial engineering to holding companies and peppercorn rents and so on - but as with every other tax there is a simply an inflection point where receipts drop to zero (if you tax income at 100%, people will simply stop working).

If you give away the land to someone else, but still own the building on it, the person you gave the land to would have to pay land value tax and they would pass that onto you in rent.

By definition the land has a market value of zero because that is what was paid for it

Who would pay money for an asset with zero returns at all (or indeed negative returns due to a bunch of administrative costs)

Rest assured, if you can extract value from something, the tax office won't value it at zero.

Neither does the market, btw.

100% LVT isn't 100% of land value it's 100% of land rents. If the bare land would rent for $2,000/month the tax is $2,000/month. You can't realistically raise the tax beyond this amount because you'd effectively be making land economically unhabitable outside of cases where the improvements were so large that you weren't significantly hindered by having some of the improvement rent absorbed.

At a 100% LVT the price of land is $0 (or more accurately equal to the price of the improvements on it). Above 100% LVT the price of land is negative so building any improvement immediately loses money and a whole host of other negative consequences.

The claim is that 100% of land rent in the US is smaller than income tax + sales tax + property tax + corporate tax. You can no longer replace every tax in the system with land rents unless you shrink the size of government.