Besides, at least in Europe free immigration would lead to massive civil unrest and possibly civil war, which would kill even more. You can not have free immigration into societies where the whole nation is ethnically defined without destabilizing them and most of the non-American world is ethnically defined. Mass migration is not a viable solution to population growth.
Nah. In the long term, societies will adapt. Sure there will be a lot of xenophobia and stupid "culture wars" in the meantime, but eventually even the most backward people will have to accept the fact that they live in a multicultural society, and there's nothing they can do to change that.