This is a popular rationale for space colonization, but the carrying capacity of the Earth remains a long way from its theoretical limits. Most of the problems people blame on overpopulation are problems of the market economy and political mismanagement. It’s just the latest way of diverting blame to the poor and brown people and their supposedly animalistic compulsions. Even given existing technology, world population growth is expected to plateau in the next 50 years --as long as we can restrain western culture’s perverse inclination to keep rationalizing poverty. Poverty and poor healthcare are the primary accelerants of population growth --because the poor tend to see children as their only form of social security and high infant mortality rates compel people to ‘hedge their bet’. The more developed societies already see negative population growth --aging populations-- because they keep infant mortality low, keep people healthy longer so their phase of economic productivity is longer and their attempts at child-rearing are later in life, and they create institutions and systems that let people rely on the state and their savings in their old age while at the same time steadily increasing the cost of raising children.
If you anticipate the technology to facilitate space colonization, you are also anticipating the technology that will increase sustainable carrying capacity on Earth. Essentially, learning to live in space means learning to go from dirt, rock, and sunlight to a middle-class standard of living using machines on the scale of home appliances. So there’s almost nothing about life right on Earth that capability would not change. That itself is a more important motivation for pursuing space settlement --as a way to accelerate that development-- than any of the rationalizations usually proposed. Learning to live in space is learning to live more sustainably on Earth --without the benign habitat Mother Nature coddles us with here.
Ultimately, a culture with the means to radically extend human lifespan will certainly face a population issue --or more of a conflict of environmental sustainability. People simply won’t die very often and so, no matter how low the birth rates, there will be growth. One could certainly evolve the Earth into a perfectly comfortable ‘ecumenopolis’, but would we as a society accept that wholesale sacrifice of the natural environment?
But by the time we reach that far-off point transhumanist lifestyle options may be common. If the older generations are mostly transhuman, they would have the option to settle, as artilects living in virtual habitats (VRcos), the inaccessible regions of the Earth --the deep interior-- as well as the interiors of all the natural bodies of the solar system without the contrivance of grand space colonies with their elaborate organic life support and costly man-rated spacecraft. Earth could comfortably be home to trillions while leaving its entire surface to one vast nature reserve. This is why it’s often suggested that one solution to the Fermi Paradox is that advanced civilizations ‘digitize’, retreat into virtual habitats, and thus become harder to detect for lack of their visible activity.
What I think is overlooked in space futurism is how much the bottom line actually rules. I think Space Race propaganda created false expectations about what governments can and will actually do. As long as we live in a culture dominated by a market economy, no significant space development is ever going to be accomplished unless it fits within that context. The bottom-line will-out, in space as on Earth. The profit motive is its only motive and whatever is the cheapest way of doing things out there is likely to become the convention by default. If that favors machine intelligence over organic life, that’s how it will go. None of those other rationalizations mean squat on Wall Street.
This may change with the advent of a post-scarcity culture that pushes society’s general concerns up Maslow’s Pyramid and affords an increasing number of small groups and individuals a new and vast industrial capability. When the general public --not just a few eccentric billionaires-- can pursue going to and homesteading in space as a hobby it will be a mainstream option. But, as I said, those people won’t be going there for any practical reasons. They will be going there for a lifestyle, and it will have to be an attractive lifestyle.