It's the same in the U.S. if you have a "Black" sounding name, you are less likely to be called in for an interview. I never understood why Black parents would give their children "ethnic" names knowing that it makes it harder in society. Even if their were only a 10% difference, why handicap your children?
And yes I'm Black.
To put it bluntly, a country doesn't get to colonize other other countries and then complain if people from those countries take the claims of civilizational superiority at face value and come to experience it for themselves. Colonization drastically and permanently altered the destiny of those countries, and unwillingness to accommodate people from those places displays a lack of responsibility.
The fact is, integrating immigrants IS an economic issue, there IS a limit, and if we fail, there WILL be backlash.
Anyhow, there's a plethora of studies that have been done on the economic impacts of migration, expected outcomes to immigrants measuring different factors (wages, employment, and subjective measures of assimilation), and so on. It's basically an entire field in itself.
What is the real 'limit'? The answer is when the negative societal effects become greater than the positive ones, and the host population decides to limit immigration.
The rest of your post was a moral argument, which again, doesn't matter when the population has decided they're at the 'limit'.