The argument against it is that a vacant property imposes very little cost upon society. It doesn't require fire protection, it doesnt add children to the education system, it doesn't use any municipal resources. If it's an eyesore or presents a hazard in some way, sure, but simply being vacant or "underutilized" doesn't do that. Why should it pay to simply exist?

> The argument against it is that a vacant property imposes very little cost upon society.

A vacant property (really, any ownership of property, period) results in an opportunity cost externalized onto all other members of society. That opportunity cost is equal to the land's value. In the middle of nowhere, therefore, that opportunity cost might be low to the point of nonexistence, but in the middle of a city downtown, that opportunity cost can be and often is on the scale of tens/hundreds of thousands of dollars (or more!) per year. That is wealth that is long overdue to be repaid back to the rest of society.

The vacant lot in the middle of Manhattan has a massive opportunity cost to society. If you goal is to own a vacant lot and you don't care where it is, trade that vacant lot in Manhattan for another one in rural Alabama.

The apartment tower also has massive costs. It requires high-capacity water, sewer, electric, and trash service. It requires specialized fire protection services including extra training and equipment to fight fires in high rise buildings. It has a massive carbon footprint.

Why should a property owner who does not impose any of those costs (or imposes a tiny fraction of them) pay equally for them?

The apartment tower is likely in a high density area already built for those types of services. It's a perfectly sensible idea to penalize those who would waste those services on a vacant lot.

> It requires high-capacity water, sewer, electric, and trash service. It requires specialized fire protection services including extra training and equipment to fight fires in high rise buildings.

The apartment almost certainly already pays for all of these things.

> It has a massive carbon footprint.

Which can be offset or even reduced/eliminated outright.

It's the greenest type of residence per capita.

It imposes the cost of pushing people farther away from each other. Every block that's empty is one block farther people have to walk/cycle/drive to get where they're going.

So you'd be in favor of plowing under Central Park and covering it with apartments towers so that everyone could be closer together?

Central Park isn't empty land; it's in active use. Also, I think an argument could be made that Central Park generates enough (intangible) value to cover its LVT. When the government pays tax to itself it nets out to zero anyway AFAIK.