They looked at total land use required to support cities and other areas and found that while the city footprint is small, the supportive infrastructure for the city is large. They found that when accounting for this, land use per capita is about the same regardless of density. Wish I could find it but there are a lot of Nature papers submitted every week.
That study doesn’t address your argument. The land use of a city isn’t simply the physical land taken up by that city. Per capita energy expenditures significantly drop as city density increases, even if we moved to solar power that would still represent land use.
The actual study is filled with it’s own problems such as ignoring land covered by water etc, but that’s largely irrelevant here. However the real issue is it’s looking at land use around cities which are rarely independent. The area around London for example isn’t a single city it’s a cluster of different cities of various densities that all bleed into each other. Is to use a US example is Patterson part of NYC? How about Stamford and or Newark? If not where exactly do you place the borders between each of them?
Looking at population in the heart of NYC vs the surrounding areas over time and they are fairly independent.
They didn't go into US cities in this analysis as far as I can see right, just chinese and european ones? Also do they focus on total ecological footprint or just land use equivalent, such as more energy usage from suburban housing, more emissions from car ownership and driving vs. things like every human needs this much farm land to feed them?
EDIT: found it https://www.nature.com/articles/s41598-021-01477-y