Most of our cities (maybe all?) haven't been planned that way though. They usually start out as a small town, then they get a large influx of people and businesses who all want different things, and the city ends up growing by leaps and bounds with very little planning. Then it happens again and again, in waves of growth. Even if the expansion was somehow planned well, the existing part of the city won't be prepared.

Also, there are plenty of reasons to travel around town that don't involve what you need in your daily life. What about when your friends want to meet at a bar on the other side of town? If that's 5 blocks, no big deal. If that's 15 miles it becomes a problem.

High population density doesn't make public transportation efficient, good planning does. If the public transportation system is designed for a city of 2 million, and the city grows to 7 million, the public transportation system won't be effifcient, or pleasant to use, at all. The unpleasantness and eneffieciency is one of the reasons so many people have cars to begin with. Private transportation takes you where you want to go, when you want to go there, in an environment of your choosing. As is mentioned in other comments here, walking when the weather is bad (cold north, too humid south) is very unpleasant no matter what.