In the United States, it was somewhat more complex than that. The highway network was and is primarily part of the nation's military defense infrastructure, so that weapons and personnel can be moved around in a time of crisis. (Something from Germany that impressed the U.S. during WWII.)

This is why the system is named after a general who was also a president ("The Eisenhower Interstate Highway System").

It's also the reason why the rails are not usually removed from abandoned railroads anymore: So they can be rehabbed in an emergency.

There's also a lot of social studies involved, including the baby boom.

Like all large human endeavors, it's messy.

[Edit to add:]

Would private roads, paid for collectively by the developers or residents of those suburbs, have helped to alleviate or reduce the problems outlined above?

One of the many contributing factors to the U.S. Civil War was the notion that the North wanted to shed its remaining privatized roads and federalize the whole thing, while the South wanted entirely private road systems.