A plot of land can only be home to several thousand people if you are willing to pay a lot of money to build it in that fashion. Building up is not a cost saving measure, it is a demand placed upon a plot of land as a consequence of population density. Building suburban homes for several thousand people will occupy more land than a dense urban apartment tower, but it will be an order of magnitude cheaper to build in the first place.
"Building up is not a cost saving measure"
There has been a consistent misreading in this thread, focusing on cost. My focus was not on cost, but on resource use. Nowhere did I suggest that cities were cheaper than the suburbs. I stated above that building in a city is pricier than building in the suburbs.
However, my point was, the suburbs use more resources. The biggest resource that is used in the suburbs is land. Per capita, the suburbs use up much more land than the cities do. The geographical dispersion leads to more resource use in the suburbs.
Consider electricity being carried over a wire. Some energy is lost for every kilometer the energy needs to be carried. In a city, you might have 100,000 people living in just a few blocks - the energy does not need to travel far, per capita. In the suburbs, the same 100,000 people might be spread out over many kilometers.
I have not mentioned the environmental impact, but we could discuss that too. The suburbs use up a lot of land. The suburbs have a major impact on forests and lakes and rivers, and the wildlife that depends on those forests and lakes and rivers.
It might help to engage in a thought experiment about how much land you could free up if all people clumped together in an urban area as dense as New York City. In the USA, the states of Maine, Vermont, New Hampshire and Massachusetts have a combined population a little over 9 million. New York City has a population a bit more than 8 million. Basically, if you wanted to pack all these people into another New York, you would have a city smaller than Massachusetts, and Maine, Vermont and New Hampshire would be pure, untouched, pristine forest. Mind you, I am not suggesting this is a practical idea, I'm simply offering this as a thought experiment, as a way of imagining some of the environmental benefits of density.
1) It feels like you are exaggerating population densities. Outside of some ultra high density areas in Manhattan, you aren't going to have 100,000 people in a few blocks. The density of most cities is about 3 to 4x that of suburbs, not orders of magnitude greater. (Note: I'm going off Bay Area data here).
2) Agreed on environmental costs not being accounted for. Developing suburbs would cost more if they were; how much I can't say.
3) On your thought experiment, here's something to think about: The entire world's population can fit in Texas (270,000 sq miles) at density levels found in SF neighborhoods. You'd need just over 3 Texases (or a Texas + Alaska) to do suburban density levels (~900,000 sq miles). But you would need about 19+ million sq miles for farming (russia + canada + us + china + brazil); in other words, the land use savings gained from going fully urban is a rounding error.
3a) On top of that, you already have to build out roads, wires, etc. to get to the farmland. When also given that the land everywhere can absorb some waste with little effect (septic tanks), it actually is efficient to spread the population more evenly throughout this hypothetical world.
4) Again the cost does matter. The interstate highway system has a lower cost per person and higher average utilization per person (defined as US residents) than San Francisco's Central subway does per person (SF residents). Ongoing maintenance still looks the same; San Francisco needs to spend about $51M a year on road maintenance. Sunnyvale is at $4.7M with a 6th of the population and a 3rd the density. There might be some resources saved in higher density, but something is dragging the per capita costs higher in highly dense areas.
Err... He capitalized "PER CAPITA".
In cities, a piece of land the size of 6 suburban homes (counting backyard) can be home to several thousand people, that's why land is expensive.
Go to Hong Kong, you'll see apartment buildings with 40 floors. On each floor there are 20 units. In each unit there are 2 rooms, a living room, a kitchen and a toilet. Each room is 2.5 metres by 2.5 metres, the living room 3 times that. Anywhere from 2 to 6 people can live in a single unit, but usually 4; The government doesn't hand out public housing with 2 rooms to only 2 people. 4 * 20 * 40 is over 3200 residents.
In the suburbs the same land is home to only around two dozen people. Thus it would make sense that in Hong Kong land could be a hundred times more expensive than in a suburb anywhere else.