You are placing a lot of weight on goodwill. It's a pretty good bet that America won't be relying on the goodwill of Mexico nor will Germany and the Nordic countries be relying on the goodwill of Syria etc at any point in the future (unless we are consumed by the waves of immigration to the point our culture is snuffed out). As for the benefit of taking in economic refuguees being helpful to the planet, I invite you all to watch this video. The primary point which is very well made is that a million immigrants isn't even a drop in the bucket on the scale of the billions of people in the world.
Looks like little dude ate shrooms and is just starting to see the fun side of the nausea wave -- so could be an appropriate post response in some D&D cases...
One also needs to take into account the country's situation. What would Mexico look like if approximately 500,000 wouldn't have been killed during a narcowar? What would illegal immigrant look like if more Mexicans had better opportunities? What would terrorism look like when more Muslims have better opportunities?
Japan's going to be an interesting case. Outside of Tokyo, they're not really used to foreigners and they've never been a country in favor of migration. Japan had issues with Japanese-Brazilian immigrants (people of Japanese ancestry born and raised in Brazil), so I can't imagine there being a smooth integration. Something has to give: they could end up like the Gulf States (bring in large migrant populations to do work but deny them rights or a path to citizenship), they could ignore/accept the problem and watch their population and economy shrink, or they could bring in foreigners. Of course, the longer they fail to act, the more migrants they will need and the worse it will become. I wouldn't be surprised if they do something similar to what the Israelis do and enact some sort of massive birth right program and start encouraging those from the Japanese diaspora to return and get citizenship.
I guess a question is by "Society", whether you're referring to American culture, and what aspects of it are one would try to preserve. Another question would be to what extent of immigration one would want to control: legal, illegal (border control/amnesty), and humanitarian.