> The problem here is that it's cheaper to leave financed buildings empty, rather than fill them up at cheaper rentsExactly! So we make it more expensive to leave their building empty. Land value tax makes it more expensive to hold the land vacant, thus encouraging the speculator to either use the property (improving the community), or continue lowering rental/sale prices until it rents or sells, or pay higher taxes to the community they're ruining.
> Empty lots aren't empty because their owners hate you, it's because the land value is too low for the mortgage and needs to drop, but can't, they're unwilling or unable to eat the loss.
They're empty because the speculators are asking so much above market price for rent or sale that nobody can afford it. The solution is to institute forces which coerce them to either use it or sell it (potentially at a loss, but not as high a loss as holding it vacant).
> Land value tax supposedly solves that ... by making everything more expensive?
No, land value tax only makes it more expensive to leave the property empty. It doesn't make anything else more expensive. Indeed, it makes it cheaper for a business to buy up an unused property, because the seller would rather sell at a loss than incur a sufficiently larger loss (land value tax) over time.