Exactly. Over the next few generations. Everyone was immediate integration, which doesn't happen in most places AFAIK. Even in America, first generation immigrants and refugees stand apart in some places. But their kids fit in well, and are fairly American, though they still possibly speak the heritage language and such. By grandkids though you couldn't tell them apart from normal 'integrated' Americans apart from the accent of their grandparents.

It just takes time to integrate, and I'd say those who argue that Europe isn't integrated are looking st more recent immigrants, or older generations, and not the ones who would most likely be integrated already.