Why the US has expensive broadband

I keep seeing all of these people whining about why the US seems to be 'behind' other countries in broadband. So I had a hypothesis: Tis NOT the evil broadband companies, but the low population density of the USA as compared to most other nations.

Population USA: ~280,000,000
Land Area USA:  3.719 Million Square Miles
Average population Density: 87.3/squre mile

Population Europe: 500,000,000
Land Area Europe: 1.67 Million Square Miles
Population Density: 265 people per square mile

Population South Korea (often cited as the 'model' country) 48.5 Million
Land Area South Korea:  38,023 Miles
Population Density:  1279 people per square mile

Finally China:

Population China: 1.35 billion people
Land Area China: 3.601 Million Square Miles
Population Density:  376 people /square mile (noting that most of china is uninhabited, so its really MUCH higher).

Hypothesis:

Low population density as related to geographic area means broadband is MUCH more expensive. You have to run correspondingly more wire, have less revenue per square mile covered, and have more infrastructure to support in order to get your population 'on the grid'.

So I don't think its 'oh the us is falling behind' but rather "We are a HUGE country, so its harder for us to have 'broadband' at cheaper prices like other countries with higher population densities.