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>and to lower their standard of living year after year, and die out as the birth rate declines

Eventually the population will get low enough that standards of living start improving because there's so much land and resources per person, and the Japanese birth rate will start rising again. Which won't happen if they keep importing foreigners to compete with Japanese youth for resources.

Lower GDP doesn't mean to lower standard of living, if it is due to lower population. Similarly, more foreigners doesn't mean better standard of living. There is no point in increasing the GDP if this doesn't translate.

Check the EU: millions of foreigner have arrived in the past 20 years, yet EU's GDP has been growing very little during the same time

Well, true.

Sigh.