I'm well aware that the "overpopulation" myth is BS and that the limits to earth's carrying capacity, if there even are such limits, have yet to be seriously explored. I'd quibble with a couple things though.
Yes, IMO, we do need "nature," because (a) that is most of what generates much of our oxygen, and (b) it is the most sensible use for much of the land in even a very densely populated world. That some of the most densely populated cities in the world (New York, Paris, Hong Kong, probably others) also find space for beautiful park systems seems to me a strong argument that we need not eliminate "nature" in order to achieve a vastly higher population or population density than we have today.
The problem of pollution will need to be addressed in a sustainable fashion. A large part of that solution will be technology. The U.S. manufactures almost as much as China today, by some measures more, yet it does so far more cleanly, because today, we can afford cleaner methods of production, while China can't. That is not a function of the number of people there, but simply their as-yet lower level of development. When they are as wealthy as we are, they'll be able to afford to produce more cleanly, and they will.
I do not believe that humans have much understanding of climate, frankly, much less that they have much influence over it on a global level. Sufficiently large cities, however, do become heat islands. We will have to use technology, and probably energy (hopefully cleanly and sustainably produced) to deal with this, especially in the parts of the world which are already hot and/or humid. Again, increasing development and hence wealth should help. If the global climate does become significantly warmer, some adjustments will be necessary, of course, but it should actually be an overall help to humanity, not a hindrance, because it will open up vast regions in the world to agriculture that cannot be done in those regions today. (It will of course reduce production in some places as well, but the net effect will be not a loss of total land suitable for agriculture but a huge, huge gain.)
One challenge we will have to tackle: the near-universal human obsession with big governments, nation-states, collectivism, and war. All of those things in their current form are incompatible with life, even life as we know it today, much less the life that could exist on a wealthier, more densely populated, more civilized planet. In fact, IMO, those things constitute the chief impediment to becoming such a world.
If all else fails, lower your standards.