What benefits do migrants bring to a country? Immigrants of some sort probably do most of the menial tasks that the vagaries of which uterus you emerged from let you avoid. They're also the doctors who treat you, your coworkers if you're in tech like most of us are, the people who cook both whatever trendy food you enjoy and whatever comfort food you enjoy. They're the people who actually believe in the fictions the West tells itself about what it is and what it wants to be. They're the people who work twice as hard as you do because they actually know the value of what you were born with and never appreciated like they did.
If we strip your comment from the emotional affect, you're essentially saying that immigrants are happy to do menial jobs that the locals do not.
How do countries without large immigrant (I won't even go to refugees) populations handle this? Switzerland seems to be doing fine. Japan isn't falling apart because there's nobody to cook. Most of Asia is doing fine without allowing any immigrants.
So on a strict analysis of whether immigrants are beneficial to the host population, your argument isn't made.
1. I don't think of foreigners who live in Switzerland as 'immigrants' (despite the article calling them that). They are foreigners who are residing in the country (and most of them come from Europe anyways). It's extremely hard to obtain Swiss citizenship.
2. All the talk about Japan economy doing badly is nonsense. If you believe that narrative (which is totally understandable as that's the conventional wisdom), I strongly suggest you read this article: http://www.nytimes.com/2012/01/08/opinion/sunday/the-true-st...
Basically many Japan watchers (ie people who live there and know the country intimately well) subscribe to this 'alternative' view.