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The US doesn't have tons of "empty space". Just about 5% of the lower 48 are wilderness untouched by humans. And the less is said about the UK and Europe, the better. Unless you mean urban sprawl creeping into rural areas, but then that'd mean some other stretch of land is going to be ruined elsewhere unless productivity increases enough to compensate for it (and even the green revolution is a dubious achievement long-term, considering the effects of top-soil degradation, imbalance in the phosphorus-nitrogen cycles and climate change).
Of course some people would be quick to jump in and defend Europe claiming forestation has grown in the last decades etc. but... I don't think Europe used to be a monoculture of symmetrically planted Norway spruces before humans. Ideally, you would want a population density similar to that of Australia, Finland or the Baltic countries to actually achieve a sustainable, zero growth civilization. But maybe it could be more as long as we develop quality artificial meat and opt for vertical farms.
