Our planet cannot support 10 billion people.
With automation and robots, we can support a population without an eternal underclass of serfs to throw their vitality into the meat grinder of capitalism.
Source needed
Food is not the limiting factor for population.
Parent post hints that X < 10B, but I'd wager many believe X < whatever we have now
It is obvious Earth could hold a very large human population - but not for very long, and not (for those people) very well
As resources like clean drinking water get more and more scarce, and climate change and the refugees it produces cause all of us to pack into smaller and smaller areas we'll need to start paying more and more attention to this to make sure that we're not destroying what resources we still have.
But then the people who own the robots won't feel special...
Instead they would line up for an overpriced apartment in London or a condo in Silicon Valley. A nice coast with view if they have the money.
It would not be easy to beat people into moving off Earth en masse, if they aren't willing to move out of metro area.
At an annual growth rate of 1%, starting from the present population in 3400 years the amount of mass we need for human bodies is equal to the combined mass of the Earth and the Moon.
In another 600 years and the mass we need for humans equals the mass of Jupiter.
From there it is only 700 years until we need the mass of the entire solar system, including the Sun, for human bodies.
From then it is about 2000 more years before we need the mass of the entire Milky Way galaxy, which is problematic because unless we have FTL travel we won't have been able to use any resources that are farther than 6700 light years from Earth, which is only a small fraction of the Milky Way.
Another 5600 years (about 12300 years from now) we need the mass of the observable universe.
Without FTL after about 12000 years at 1% annual growth the amount of space we could theoretically have access to (a sphere of radius 12000 light years around the Earth) does not have enough space to hold everybody. The volume of that sphere divided by the population would fall below 0.006 m^3, which is about how much volume a human body takes up. (And we can't actually pack people that densely because we are not actually a shape that packs well).
How about energy, rather than mass or space? If our energy needs grow by 1% per year in about 9300 years our annual energy consumption will be equal to the total energy of the Milky Way. By "total energy of the Milky Way" I mean what we could get if all of it were converted to energy (E=mc^2).
In 12000 years we'd need the energy of the entire freaking observable universe.
That people who have to fight each other just for clean water and food will focus on building guns and bombs instead of spaceships and won't have the time or resources to search for suitable planets.