Unfortunately, it does not really work.

* The denser the area, the slower the transportation (by any mean).

* People in dense areas spend more time commuting than people in sparse areas.

* When you upgrade the infrastructure making transportation faster, people move farther, keeping their commuting time constant.

It's just that packing people around the same area is not a very good idea, whichever way you do it; there is no true solution to the problems it causes.

The problem with that is that large metros in general have dramatically healthier job markets. If your choice is either (a) live in a sparsely populated place with no job at all but not much traffic, or (b) move to the affordable outskirts of a metro area with a hellish commute, a sizable proportion of people end up choosing b.

There isn’t really a “good idea” alternative to packing people around the same area; higher density is dramatically more cost-efficient for providing the same quality of public services and infrastructure and the same kinds of employment opportunities.

The question then becomes: if n people are going to live in the metro area, where someone in any nearby housing might plausibly work at any nearby job, what is the most convenient and effective way of organizing the space? The answer is: put a high density of housing and jobs directly next to transit corridors, so that many people can find work within a reasonable commute from their house (or can find housing within a reasonable commute from their jobs) without creating traffic bottlenecks. If instead you follow the LA model where density is mostly uniformly low, and commuting is via low-bandwidth freeways, then what you end up with is people living 2 hours from downtown and leaving home at 4 AM every day to beat the traffic, and other people stuck crawling down the highway twice a day.

Why do you think that the transportation speed is inversely related to density? I can ride my bike at approximately the same speed in the city as I can in the countryside. It's just that in the city I can reach anything I need within 30 minutes.

This might be true for a particular city depending on population density and commute habits of the people, but after a certain population density is reached the premise that transportation speed is inversely proportional to density holds true for the most part. Fixed line transport such as trains may not be directly affected by the density but there may be a bottleneck if the density is sufficient to saturate the lines. If the trains are running full - this would lead to increase in wait times and longer commute time.

If you fill your whole city with 30+ story high rises and subways are overwhelmed even when running cars every 1-2 minutes (e.g. some Chinese cities), you can definitely create a bottleneck at the subway during commute hours. That's very high density we are talking about though.