But you're describing a city. The graphic does not show a city, it shows one apartment building. The rest of the city you've described would swallow the rest of the green space. That's what sprawl is, when the desirable land becomes more valuable so nearby land is further developed and becomes more valuable becomes more developed becomes more valuable.
It's an inperfect metaphor anyway, because island development works under its own constraints. An island can only support so many people, regardless of whether they live in an apartment or a single family home. There are limits, and growing beyond those limits will result in feedback loop which can cause systemic collapse. See: San Francisco, where retailers must raise prices because they cannot afford to hire someone who can afford to live there because everything is so expensive.
I'm with you that we need more walkable cities. But car-dependent development is a result of regulatory capture by land developers. Zoning and public transit spending are the battles we need to win. And if we can tax corporate landlords out of existence, that would go a long way, too.