Because culture is not an abstract set of ideas separate from its people. You can only adopt a culture you weren't brought up in to a certain degree, and usually very shallowly.
Seems like a lack of faith in societies to properly integrate new arrivals.
Yes, exactly. I have little faith in that, because it rarely happens.
And are you aware that international migration has been happening for millennia? All nations have people who have assimilated and integrated, to different degrees.