Those houses built in-ground with an exposed southerly wall are another form of an Earthship and they can come in pretty much any shape and size.
New York City has pretty much utilized a lot of its underground space, but there are a few problems building underground. One is the water table - once you hit that, everything will want to fill with water. Disrupting that water table for the purpose of building is a death sentence for every living thing that relies on that water. If you're thining on a global scale, that means risk of contamination for most of the world's water supply.
Another is exposing minerals, elements and materials that were not meant to be exposed... at least not without toxic repercussions. There are a lot of things buried underground that should really stay underground - uranium, oil, coal, etc. Even though we use those particular ones, look at the mess they've made on the surface.
Last is ventilation. Where are all the excess gasses we create going? I lived near Bisbee Arizona. There was an old copper mine they gave tours of out there. In less than 5 minutes the tour guide rattled off about a dozen hazards of living and working underground like those workers did. The only one he said that ine didn't have was a heat problem since the ventilation of the mountain it was built in pulled the air through, most underground mines would reach over100 degrees easily though.
An entire city underground would probably have weather about the equivalent of a Phoenix Summer, year-round... only with a lot of extra moisture thrown in and worse air quality!