It doesn't mean high(er) density living at all (at least not how it is understood in the rest of the world). The US is mostly empty space, no flats or whatever required.
Higher density happens because investors want to maximize the use of land in desirable areas, not because land is unavailable or difficult to zone. I live in Bucharest, a city of incredibly high RE development, and most of the new buildings are more compressed and crowded in on each other than they were under communism, which is a common occurrence in the former Soviet satellite states [1].
From my window, I can see across the Delta Vacaresti, a wildlife reserve that was once a neighborhood that Ceausescu just had time to raze to the ground for some new insane scheme before his people shot him. Across the way, I see three massive multistory residential blocks going up, crowded together like pedestrians on a metro train at rush hour - only one side of the front-most block has any view of the Delta, while the others literally live in each other's shadows, lacking sunlight.
By contrast, communist design principles designed a whole neighborhood, with schools and hospitals and doctors, with the 'megablocks' seen as small cities in themselves that needed dedicated support systems.
