You premises are wrong:
You define "crowded" one way, and claim Kurtzweil does not follow (your rather arbitrary definition).
You seem to equate "nature" with "unused bits of land (by humans)", thats wrong, because humans are part of nature, even if you re-define nature to mean something like "all life except humans", then wrong too, because every bit of surface of this planet has been touched by humans, and is therefore "used" by humans. The ocean is where we store our unwanted plastc, the Arctic and Antarctic is where we power our global airconditioning. (Mind you we have limited ice supply, hence its time limited airco)
So Kurtzweil must mean something like "unsused for habitation (aka: not cities)" So the issue becomes humans could use the planet far more efficiently then we do now for habitation. Its easy to see that we could form a few more London/Paris/New York's right here in The Netherlands and we could house many more people.
Now, thee shit will hit the fan with regards to some resources (Where will the energy come from), but the resource we actually have plenty of is space... we still can go UP and DOWN, and we can even get rid of some of those "single tree that is allowed to fall down after a meeting"