For example, one can build 30 story (plus 10 underground for parking/storage/etc...) towers with enough green space around it instead of covering all available space with the 3 story-s.
https://en.wikipedia.org/wiki/Le_Corbusier#Criticism
Good urban space is mostly about how nice it feels to be on a street. You want a comfortable amount of walking space, destinations that are close together, and that's pretty much it. Surrounding buildings with parks makes walking harder and less pleasant.
There's probably enough demand for taller buildings, but it's illegal.
on 2D surface the density can be done only by growing into the 3rd dimension. The only issue is how to do it. The ratio between height, footprint and total capacity i think reaches its worst value in the current style of development in the Valley (as a result of developers ripping best value in profit possible inside the municipally imposed limits)
>Surrounding buildings with parks makes walking harder and less pleasant.
as if walking on a concrete sidewalk between 3-story wall and the traffic lanes in the open under CA midday Sun beats it :)
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.
For apartment complexes, the towers surrounded by park concept is the standard way to build new apartments in Korea for over a decade now. It works well because the density of residents attract businesses to the outskirts of the park, and in the parks I've seen, they always contain multiple playgrounds, rest areas, sculptures, and exercise equipment for public use. Children play there after school, families gather on weekends, and street markets and street fairs are held in the parks on a regular basis. It is a very efficient use of land to provide both urban density and public space. (Here is a typical apartment complex design: http://image.apt.joinsland.com/contents.upload/1501/1945/bir...)