Doesn't Seoul have a huge belt of mountains to go skiing and hiking in just a couple miles outside the outer subway stations? Maybe even closer around places like Seouldae? That's a pretty good option for open space.
I agree that US suburbia is stifling in its own way and hostile to transit and dollar vans. Still, LA, SF, Chicago, and NYC have plenty of places they could work.
Those density figures are misleading. You've chosen San Francisco County, LA county, and the five central NY counties, but included only the populated part of Seoul and most of the Kaanto for Tokyo. The populated parts of Tokyo and Seoul are of similar density (as is Mexico City), around 40k/mi^2, fairly consistently through their metro areas. New York varies from 110k in central Manhattan to miles low density 4k sprawl on the outskirts. SF tops out around 17k and then sprawls. LA is similar but slightly more consistent. The pretty parts of Paris are at 80k but everyone finds them liberating and exciting rather than stifling -- maybe because it's done without high rises.