The "3-story barracks" you speak of - they're actually the most humane compromise we have. Something that is relatively cost-effective to throw up, but accommodates a decent number of people, and when built throughout a neighborhood will easily pass the critical thresholds for future services. Much of San Francisco is also built to 3 stories, and it's one of the most dense areas in the country. It's a geometry problem, as you point out - but also a cost problem. It's cheaper to have mid-rises everywhere than a few high rises, and people find shorter constructions more humane on average. But the construction height isn't the _only_ thing to worry about.

Land use in suburban areas is mostly premised on maximizing car traffic. That's why we have the big six-lane streets and the huge parking lots with sad, small strips of grass separating everything. If we optimize for maximizing people movement over car movement, the streets get smaller and so do the parking lots; transit and bikes get more accommodation. Room opens up for more destinations, and you get more access at a lower average speed and energy consumption, further improving the land value - all just by changing the design requirements. Traditional cities are very energy-efficient.