you're acting as though an immigrant from any of the dense population centers has the same impact as a native-born child on the culture and economy. that is false. sometimes it's for the better (in America, we have many well-educated immigrants from India and China). sometimes it's for the worse (see Europe's struggles with uneducated muslim immigrants from north Africa and the Middle East).

importing large groups of people sometimes works; we did it pretty well in America because we had so much room to grow. transportation and communication were also much harder, so it was less easy for people to maintain ties to their former country and family there; they adapted a little more, though ethnic ghettos were still a problem.

it's not an intractable problem but saying "just get immigrants bro" isn't really a good solution. we are sometimes biased in the US because we are selective (too much so, I think). we bring in the best from high-population areas like Africa and India and we see benefits for that. on the other hand, while migrant working and a moderate level of illegal immigration are fine and even economically beneficial, it would be silly to deny that the current levels are causing severe problems. when you lose that selectivity and control, things don't turn out so well. and to import enough people to make up for falling birthrates we would have to broaden our horizons beyond skilled workers.