That nation is not falling apart because of population growth what are you on about. It's falling apart because its human capital stinks. Those are not one and the same.
Australia has the highest population growth rate in the Western World, you probably think it's on the bring of collapse or will be if it continues this path, yet they are trying to turn it into another America over the long-term (excluding that lowest rung of human capital the US is now stuck with for all time). And yet if we are alive in your techno-future immortal world in 100 years we are gonna be fucking cursing our 'luck' about the USA (United States of Australia), with it's couple hundred million Anglos that now have to be dealt with in addition to the US if it's still functioning. Great!
It won't be luck though, we know it's happening right before our very own eyes, but we have people today right now denying the reality.
Look, Chinese are capable people and I don't think having less of them is going to be the solution until we really do have the tech you claim is going to exist (with apparently 100% certainty on your part). You are gambling with the demographic future of the Chinese people. You want to end up like Japan?
Japanese have been coping this same shit since the 1980s, about the robots that are coming to save them any day now from aging. How's Japan looking now? With each passing decade the relative power difference between them and the US expands. People forget that Japan had close the population of the US at one point! And had the level of economic influence that pretty much equaled it!
Due to the petrodollar hegemony, the US standard of living is propped up artificially by basically the entire world.... and its a taxation on all the other nations of the world due to the US dollar reserve currency status...
in order for US to increase its population by three times as you suggested, and if it hopes to even resemble anything close to its current (already faltering) lifestyle/way of life,
it would need another three earths to colonize in order to prop up the "exorbitant" privilege!
Even if China makes no other changes, giving its current trajectory, in the future China will have WAY more people that are jobless than people who have a job, because all the menial labor jobs, even most of the "professional" jobs, will be either been done away with, displaced, and/or in some fashion or another eclipsed or made obsolete by the combination of AI and automation advancement and restructurings of the future...
the overwhelming worry is too many people and not enough jobs, not too many jobs and not enough people... anyone who cannot see this obvious trend has blinders on and are in denial of the facts of reality... a near fully automated society of the future China can maintain its GDP with maybe only 10% of the current workforce it has now... what are the other 90% going to do? And you want there to be more people? for what?
Given the realities of Peak Oil, of declining EROEI energy thresholds, and of climate change, ecological depletion and other realities to the limits of earth's resource and carrying capacities, it is already the case that the rate limiting factor to growth is not human population or even AI productivity nor "efficiency savings" but rather the limits to available resources that can be brought to use... With that understanding, every civilization should strive for conservation and also automation, to get the most productivity out of the minimum resources expended and to have a population level just large enough to maintain a high standard of living but not so large in excess that it starts contributing to more than necessary rapid depletion of earth remaining energy and resources that are required to achieve that standard of living /per capita in the first place... put simply,
with AI we can have the best of both worlds in terms of a wealthy per capita lifestyle whilst maintaining a very low global population so that we can mitigate and manage the remaining resources we have left on earth whilst affording everyone a relatively higher standard of living / gdp per capita etc .... to propose a race to infinite in terms of human population growth when we already have 8 billion mouths to feed on earth is absolute madness and sheer crazy