While this may seem true based on the past, any and all projections for two or three generations ahead are a complete nonsense, irrelevant and just plain wrong (more an interesting subject for sociologists, philosophers, demographic studies, than for any serious projection debates).
Couple of things that are missing in such statements (but all these are more relevant than any simulation based on past data):
1… it’s not a secret, that for our master (on the West) not enough working force is NOT an issue in the future (this may be the subject for the elected puppets on their temporary jobs who are loud when camera is recording, but not for those who run the show); even contrary, those would wish to limit the population as much as possible (noone is really worry about a ‘collapse’ of that kind, but contrary, they wish for the opposite); they openly talk about 1B or even half of that to be max for the planet.
2… Desiring a lot of work force (or even depending on it) is clearly a thing from the past, not for the future. We are just years before nearly everything will be done by machines. It means the production is not in question; work force not needed. If work force is not needed, then too many mouths are excessive, not optimal, should be reduced. In all history the work force was extremely important, tomorrow will not be anymore.
3… Similarly, fear of not having enough market (to sell) is clearly becoming a thing from the past. The system they are forcing us into is corporatism, where corporations run the show, not governments or countries. They dictate the rules, eliminate the competition, they will force you doing things you never would otherwise, they strive for a monopoly. This eliminates the need of being competitive, free market, free will, capitalism, democracy.
4… On top the world is at the end of one cycle and a new power is emerging. This kind of change is never peaceful, but turbulent and it often involves wars, hunger, devastation (meaning again noone is thinking about the collapse of not having enough children).
Industrialized countries will not collapse because of not enough children to feed the eldery; that’s just a myth. The US wouldn’t collapse is it had only 80M people and 20M of that would be 65+, neither would China if it only had 300M; the world will collapse because of other things.
(and finally, if really that would be so enormous problem, wouldn’t it be very easy to solve this problem and prevent the collapse? And they could achieve that even without any immigration if that was the goal). Nothing at all is pointing out that this is a serious problem or that it couldn’t be overcome.