Unfortunately, it is true that a fair amount of government expenses are not useful. (i.e. do not constitute a public good in the economic sense)
Also in some cases (often with environmental spending) there is an external downward pressure on land value that is offset by an increase but you don't necessarily get an increase from the original neutral value if the pollution didn't occur.
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.
Who would pay money for an asset with zero returns at all (or indeed negative returns due to a bunch of administrative costs)
Neither does the market, btw.
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.