As a European who has lived among Americans I noticed this too. It might be about finding roots and identity in a place that has a cultural canon of its own by now but tends to borrow a lot from the many incoming cultural influences. Even after more than two centuries there seems to be a fascination with the history of the Old World...the city of Damascus was first settled in the second millennium BC, just to name one extreme example. I am not denying previously existing native civilizations, only saying that you don't seem to see yourself as a continuation of that line (for rather obvious reasons).
My history teacher at my American high school had a Swedish flag in his class room because he considered himself Swedish in that one of his grandfathers was born there. That struck me as an exotic thing to do.
Family history can be fascinating, but it doesn't come up here the same way it seems to on your side of the Atlantic.
Speaking of which, Peguy, I first thought you were Polish-Polish until you explained later on that you were Polish-American. When I first got to know you I imagined a guy sitting behind a computer somewhere in Kraków....because I took your statement "I'm Polish" literarily. That's the most fascinating part of it, people saying "I'm Italian" and obviously meaning "I am an American with Italian roots", not "I identify myself as an Italian mysteriously held captive in the body of somebody born in New Jersey".