Older US cities have many of the same characteristics as cities in other parts of the world. Those characteristics can vary, from small single-family homes tightly packed into a walkable neighborhood to large scale apartment dwelling with city squares and boulevards nearby.
Americans used to build cities this way. Whether it was Moses or the emergence of a general dislike of each other, or a multitude of other possible reasons, we generally no longer do.
Moreover, many of those older city neighborhoods are considered extremely desirable to live in, even today, so much so that they have become very exclusive areas available only to those with plenty of income or wealth. That doesn't imply that most Americans would necessarily make that choice even if they could, but the continued elevation of housing costs in the best of these "old world" neighborhoods suggests to me that your thesis is at best incomplete and at worst just incorrect.