Except there is? Carrying capacity is not 'how many people can you squeeze into a location' or where there's free space to put houses, it's how many human beings the planet can support at current consumption levels. The answer to that varies by baseline, and resource (some resources renew, some don't) but as it is our current world population is consuming way more than the Earth can provide year to year, and have made few gains in reversing that trend. Yeah there's a lot of unused space on the planet, but a lot of that space isn't particularly usable to begin with.
It's a two fold problem because post-industrial nations are huge resource consumers, using up more per capita and overall than developing nations (not you China, don't play the "We're still developing!" card). While those developing nations have much higher population growth, that growth is lower impact than the existing populations in places like the USA. One American kid has a much larger impact than one in a developing nation. The big "BUT!" is that those same developing nations also work to improve living standards (as they should), and as standards go up in most cases consumption skyrockets as well.
So we're already stuck with a world population that can't all live at USA standards, but where everyone wants to live by those standards, and we're not moving fast enough to make the standards we aspire to sustainable.