That’s part of it, but the reason that’s what gets built is because it’s the main type of housing they can profitably build, and if projects are clearly unprofitable then builders and developers won’t build them. In large part, that’s a matter of codes and zoning and lots of weird local rules in each place creating all sorts barriers that drive up per-unit costs.
In a saner world that was actually trying to make things better, “Rich people want to own homes in our city, and not use them or any nearby public infrastructure, but pay us lots of property taxes we can use for the benefit of other residents,” really isn’t the kind of thing that other residents should have to see as a problem.
Instead, lots of people want to move to NYC (and other cities) and its suburbs, lots of barriers make sure there aren’t enough new homes being built to accommodate them all, so they bid up prices for the limited pool of options. I maintain that if the big buildings full of empty apartments hadn’t been built, the result wouldn’t look like “We built more and cheaper housing instead.” It would look like “We didn’t build nearly as much housing, everyone else is basically competing for the same units still, and the property tax base is smaller.”
