Partial Sentence: Countries can increase their population through immigration without increasing domestic birth rates. Countries can decrease their domestic birth rates without decreasing immigration.

Global Sentence: Global Population = People born.

Once every country is pro immigration without being pro birth there will not be enough births to maintain the current population. The can is being kicked down the road.

The problem isn't the shrinking population though. It's the aging of the entire world. Someone has to take care of these people or they die alone with nobody to attend their funeral.

The truth is letting people die by the millions in a war tends to take care of problems like this.