Canada has always accepted immigrants. Rapidly increasing the number of foreign students to goose the slumping post-secondary education sector did not work out great. Even with the reductions, there are always immigrants coming into Canada.
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.
but it's a problem easily solved by just letting in more immigrants.