If — and it's a big if because civil infrastructure is a lot more than just domiciles and a bit of tarmac to travel on — it were done right, the metro areas could expand. And many have, which is why we're increasingly urban as a species.

Sure, still technically finite, but even just at the Netherlands' population density, we could fit the world population into 1/10th of the world's land area, so it isn't a real constraint.

In most metro areas, zoning is the limiter, not land. You could quickly double the housing supply if you allow townhomes, duplexes, and small apartment buildings in areas currently captive to single family homes.

It's popular opinion expressed here that single family zoning is the only thing limiting supply. I'm not sure it's correct. There's a limited amount of construction capacity in every given area. Limited amount of construction labor (construction workers, engineers, managers), construction equipment and materials. It's not easy to scale it up. Upzoning is not a panacea.

Then normal market forces take over - as demand for extra construction equipment and materials increases, people realise they can make money there, so supply increases. It takes time and certainty, but there's nothing inherently stopping people building more cranes or training more electricians.

You can fit a hell of a lot of living space in 1 acre if you use it well. Decent mass transit also increases the effective space of the city from a job perspective

London density could easily be that of Westminster (the borough with large open areas such as Hyde Park, Green Park, St James Gardens, most of Regents Park etc -- imagine all London boroughs having that much public open space).

Westminster isn't even particularly dense, but that alone would allow an extra 6 million people to live in Greater London.

Go for Manhattan density and that's 3 times Westminster, allowing 45 million in Greater London.