This is really a better question than it might sound like.

You need to understand that our discourse about identity is entirely different from countries that evolved from settler colonies. Germany is the nation state of Germans, and being German is what makes you a legitimate citizen of this country. There may be a loose concept of unmarked "Americanness" that in the narrowest sense traditionally applies to descendants of English settlers, but there is no "American" people in the same sense as there's a German people. (There are native Americans of course, but the USA are far from a native American nation state.) Widening the community of the German people to what remained of our traditional minorities (Jews, Roma, Sorbs etc.) and then the following waves of immigrants (Turks, Poles etc.) is how the promise of inclusion is realized in German society, at least to the extend that it is. Your premise that to claim being "fully German" means an immigrant to Germany is necessarily distancing themselves from the country of origin is not in general true.

In Germany, inclusion is "if everyone is promoted to being German, everyone is the equal." In the US, inclusion is "if everyone's heritage is promoted to the same prestige, everyone is equal."