>Density brings costs of its own, though

That's very self-evident. What matters is that density means costs rise at a slower rate than income and because density tends to raise prices (the area is more desirable all else equal).

Most of the cost of installing water pipes is in digging up the street and paying people to lay the pipes. By comparison putting in a small pipe costs the same as a huge one. Suburbs need small pipes spread over a larger distance to reach X people. High-rises need large pipes over a much smaller distance to reach the same number of people. Even if you assume property values per person were identical and taxes identical the dense area has a massive cost advantage.

"There's a reason everything is more expensive in dense areas."

Often, that reason is "there's a strong market preference for density, but supply is artificially restricted by parking minimums and zoning regulations put in place by property owners who wish to maximize the value of their asset"

And this article brings up that one reason it is more expensive is that dense areas subsidize less dense areas of a city.

Actually, dense stuff is mostly cheaper until you start building way up. Tons of Italy is pretty dense and is not all that expensive in the grand scheme of things. It's also very livable and walkable. Same goes for many other places in Europe.