> They're unproductive because they suffer from a large language barrier,
Immigrants everywhere come with a language barrier. If you live in the US, very probably your ancestors did. It's the same with every first generation from everywhere.
The barriers are not all the same.
Somebody moving from Norway or Sweden will have a much easier time picking up Danish. And European immigrants are highly likely to speak English, meaning they can communicate with Danes who speak English (virtually all of them) from day one.
You're really struggling to find problems. English is spoken all over the world - people all over the world learn it, in China, India ... places with completely unrelated languages.
Immigrants everywhere come with a language barrier. If you live in the US, very probably your ancestors did. It's the same with every first generation from everywhere.