Asimov and Population Density

For today's nerd break, let's consider Isaac Asimov's The Caves of Steel, an excellent sci-fi novel sadly undermined by a failure to really grasp population density. The setting for the novel is a future version of earth in which the existence of advanced technology has failed to stem a decline in living standards (on the planet Earth, that is, the Spacers are better off than we are). The trouble is that the proposed population of Earth -- 8 billion -- is way to low to produce the effects Asimov is concerned with. Humanity, in this vision of the future, lives in giant, mostly underground mega-cities the better to leave the surface of the planet available for the exploitation of natural resources. As Wikipedia explains:

The eponymous "caves of steel" are vast city complexes covered by huge metal domes, capable of supporting tens of millions each. The New York City of that era, for example, encompasses present-day New York State, as well as large tracts of New Jersey.

But here's the thing. Present-day New York State encompasses 54,520 square miles and present-day New York City contains 27,000 people per square mile, so you'd be talking about 1.47 billion people in New York alone. And that's ignoring the "large tracts of New Jersey." What's more, that's Asimov's NYC has the same population density as present-day NYC. If instead you assume it contains Manhattan's 66,940 people per square mile, you could fit 3.652 billion people in New York State (again, we're ignoring the New Jersey Sectors). But Asimov suggests that the population density of his NYC should be even higher than that:

To be sure, something had existed in the same geographic area before then that had been called New York City. That primitive gathering of population had existed for three thousand years, not three hundred, but it hadn't been a City.

There were no Cities then. There were just huddles of dwelling places large and small, open to the air. They were something like the Spacers' Domes, only much different, of course. These huddles (the largest barely reached ten million in population and most never reached one million) were scattered all over Earth by the thousands. By modern standard, they had been completely inefficient, economicaly. [...]

For that matter, take the simple folly of endless duplication of kitchens and bathrooms as compared with the thoroughly efficient diners and shower rooms made possible by City culture.

People live in some pretty small apartments in Manhattan, but they haven't adopted collective kitchens. Nevertheless, even sticking with the Manhattan assumption, the single City contains over 1/6th of the world's population and it's not even the biggest City. Under the circumstances, it's very hard to imagine what could have compelled people to adopt the City revolution with hyper-density measures like collective kitchens. If the entire United States had the population density of an inner-ring suburb like Westchester County you could fit almost 8 billion within our borders.