Do states import immigrants because they want to make the world a better place, ir because they want to fix their own broken birth rates and prevent the country from dying out?

I think no state takes in immigrants for humanitarian reasons. They all do it because some spreadsheet warrior has calculated that each dollar invested into an immigrant, the immigrant will eventually bet the state many more dollars in tax money.

Of course those calculations are hugely flawed, similar to our climate models or Keynesian economic models. 

 It’s not for humanitarian reasons in the end (although the idiots implementing it at a middle management level beleive that shit).
The ultimate goal is to increase the number of cattle to harvest tax from, and to replace the home population.
Immigration is a weapon of war