[logfromblammo]

The limiting factor is not land area, but the marginal cost to serve an additional subscriber. It isn't the size of your graph, but the total cost of your spanning tree. The numbers involved are linear distances and number of nodes, not areas.

In most areas of the US, pre-existing infrastructure, such as improved roads and utility easements, makes serving additional customers relatively low cost. But monopolies and commodity suppliers operate at different supply points. A monopoly will intentionally reduce output below the point where marginal cost equals marginal revenue, to achieve higher prices and economic profits.

Leaving aside the concept of natural monopoly, that's the one reason. Most telecom markets are a local monopoly. Service sucks because the company providing it makes more money that way.

Land area and population density are red herrings. You need to measure the size of existing networks, such as roads, electric power, potable water and sewers, and divide those by the number of people served.

To use a car analogy, think about the Autobahn-style Interstate highway system. Before and after it was constructed, places remain the same absolute distance apart. But afterward, traveling between those places could take more or less time. Places that were previously adjacent might now require a detour via an overpass, whereas places previously distant might both have convenient on and off ramps. Travel times by car are thus determined by the roads network topology and not purely geographical distribution.

[danielweber]

Land area and population density are red herrings

No, when trying to wire up a population, population density really really matters. The #1 and #2 countries for Internet speed are Singapore and Hong Kong.

[logfromblammo]

Only in the sense that high population density makes minimal spanning trees very small indeed. The area simply is not relevant for wired coverage. Wireless links are another story, obviously, where antennas define a coverage area, but as long as the bits go through linear fibers, it simply does not matter how large someone's back yard is, or how far it extends from the front door. That area is irrelevant to the provision of service (unless someone lives on the other side of it).

The fastest data networks are wired, and even the wireless networks have linear backhaul.

By topology, a high-rise apartment building where everyone is within 100m of the utility closet on their floor is not all that different from a small town where most houses are within 100m of Main Street. The apartments have smaller area because people are stacked on top of each other. The total length of the cables and the equipment at the distribution nodes are still what matters.

You are removing a step in the causality chain. High population density causes efficient networks because all high-density areas incorporate their vertical space, by necessity. High-rise apartment and office buildings make it relatively easy to wire up a lot of people all at once.

But low population density does not necessarily imply a costly, inefficient network. The correlation between the two is stronger at the dense end of the scale. In the case where information about network topology is not available, population density may be used as a less accurate substitute, but your conclusions will likewise be less accurate, especially at the lower end of the scale.

Probably a closer approximation could be reached by looking at aerial photos of the places under comparison, adding up the total length of visible streets, and dividing population totals by that number, to get people per street-meter rather than people per square-meter.