Ventura County, California, where I grew up, would be perfect for this sort of concept... They have ten small-to-moderate-sized cities, each surrounded either by undeveloped hills, or priceless super-fertile farmland. The county has restricted urban growth to the point where any new land developments are put to a vote, and are often voted down. There is thus an artificial housing shortage, and land values remain quite high, even in our economic downturn. The only alternative now is verticality... The idea of the Farmer's Apartments tower could very well be replicated there in coming decades (albeit with a classier design, I hope).
I think that the answer to your question, however, is that, given the freedom to do so, the majority of Americans have decided that they would prefer a home of their own, with their own little speck of land, to do with as they please. The wealthier you are, the more land you can get. This has been true throughout history, but America's brand of personal liberty, government policies and economic power have made it possible for a larger portion of the population to achieve that than ever before. There is a significant and growing demand for more traditional and dense urban patterns, as well, though. I think there's a legitimate place in our urban areas for all levels of density.