Not decline, but Australia considered its population too small after the Second World War and very successfully integrated immigrants from an increasing diversity of source countries: https://en.wikipedia.org/wiki/Post-war_immigration_to_Austra...

there’s a lot less to lose when your native population is a bunch of criminals and convicts

Both New Zealand and Australia have about 30% of the population born overseas. Immigration does lead to some stresses but it also has bonuses. Immigration seems to clearly help in the short term.

But yes, immigration doesn't solve the demographics issue, because immigrant citizens also get old and expect government support.

Immigrants do often have good sized families so that brings in a fresh generation of New Zealanders. Plenty of my married friends are from mixed cultures.

In some cultures their children give more time to care for their own parents or elderly family. New Zealand born children seem less likely to do so.

The local born often whine because whinging is a significant part of our colonial heritage from England.

Japan is already accepting immigrants! It's right there in the article I linked! It's just a question of raising the quota slightly.

It's hardly going to solve every problem, it will keep restaurants from closing.

"allowing to enter the country" and "accepting" are two very distinct things.