So, Australia, despite it's reputation, as of a few years ago, had 28% of it's population born overseas. Remove the brits (6%) and the kiwis (1%), and the figure becomes 21%. Compare to 14% for the US, and 12% for the UK (without any groups removed). The last few years, the #1 source of migrants was China. Australia also has only around the replacement birthrate, and yet has increased it's population from 19M in 1999 to 24M today - a figure mostly risen on the back of migration. I'm 43 years old; the White Australia Policy finished it's 20-year dismantling the year I was born, and so has been dead as a dodo for a while now.
Canada (20% foreign-born) and New Zealand (25% foreign-born) are in similar boats. However, your statement is also pretty offensive to kiwis, of whom 15% are of Maori stock - indeed, the relatively harmonious relations are rightfully a source of pride to the kiwis. Both of these countries also deal in bilingual politics (Australia does not).
I'm less knowledgable on the makeup of the Nordic countries, but it's worth pointing out that only two western democracies have a higher rate of immigration than Australia (excluding the year of Syria crisis migration). These countries are Spain and Norway. As for Sweden (usually the go-to country for these discussions), looking now, and excluding the Syria crisis, 14% of Swedes were of foreign birth, equivalent to the US, and two-thirds of these were born outside the EU. While, yes, Sweden doesn't have the latino or black analogues in their national background like the US does, they're not as culturally homogenous as most people think.
In short, I think you're talking about the stereotypes in your head rather than the actual nations. Handwaving it away with "meh, they're all the same in those countries" is an egregious error - after all, if what you're suggesting was true, then Portugal and Ireland (95%+ local-born, single culture) would be powerhouses.