I don't think it's so much about density as it is about planning. Even in a massive area, the correct way to distrubute people in it is so that they can access what they need with ease. Let people live next to the store, their office, the bus stop and so on. How far apart clusters of people are will determine the overall density. Density doesn't say much about whether people are clustered or more evenly spread out however.
It may be hard for people in many places to grasp, but even in eastern states there are many, many areas where you could pick a direction and walk many miles without seeing anyone.
Below a certain population density (likely in the hundreds to low thousands per square mile), public transportation simply is not feasible.