It's funny because in my great great grandfather's journals he hopes his kids would be Americans and not his former nationality, or at least that's what I have been told it said as I cannot read his primary language.

I'm as basic-white-belgian as they come and even I have a little bit of Italian and Eastern European (IIRC) somewhere in there. "Pure" (ew) lineages are actually quite rare in Europe, only the most remote places were spared the millennia of warfare (and the grim reality that soldiers, uh, move genes around) and the urban flights of the industrial revolutions. The average European's background isn't as diverse as the average American's, but a lot more than one might naively assume.

What is striking about North America though is the anglo-saxon cultural homogeneity, especially considering the diverse backgrounds. Besides Quebec there's virtually no language barrier anywhere, and an almost entirely homogenous culture. You could probably raise a kid in 6 states and 3 provinces without any major issue. All North Americans eat Mac and Cheese and they all watch the Superbowl and all American children stand up for the Pledge. Meanwhile the only cultural references I am likely to have in common with the average Pole is American TV/movies/music and depending on their English skill having a conversation at all may be a major challenge.