I'm an American of European descent. Six of my eight great-grandparents were immigrants from Europe, the countries they came from being Ireland, Germany, and Austria-Hungary. I'm also descended from a Scottish couple who immigrated in the 1840s, and I'm also descended from Francis Cooke, an English Mayflower passenger.
As you can see, I'm aware of what countries my ancestors immigrated from, and yes, I find it interesting, to a point. So do many Americans, to a point. It's fun to know. But, like most Americans, I don't feel that this knowledge makes me German or Irish or English or Scottish or Eastern European. I identify as an American, first and foremost. The US is my country, the US is what I know, the US is what I identify with, and the US is what I love. I've been to Europe several times, though never to Ireland or Eastern Europe. I have been to England and Germany. In no way did I feel that I was connecting with my roots by travelling to Europe. I felt like a foreigner when I was in Europe. The people and the countries felt foreign to me. How could it be any different? How on earth could going to Europe connect me with my roots when I was born and grew up in the US, and I had parents who never traveled outside the US and three of my grandparents had never traveled outside the US? The only way I feel more connected to my roots is to travel from where I now live in South Carolina to my hometown in New Jersey.
I lived in Australia for a year. It's a fine country, but it wasn't my home. I suffered a few pangs of homesickness, but what I suffered was nothing compared to the other Americans who were there. They traveled back to visit the US (I never did, mainly due to fear of flying) and I remember that one of them, on the day before she was due to leave for a visit, had tears in her eyes at the anticipation. When I did return, I can remember looking out the window as the plane landed in LA and feeling my heart swell because I was back home. Does this sound like the reactions of people who think they are culture-less?
The USA has a culture. It seems to be criticized far more often than the cultures of other countries, but be that as it may, it has one. I don't believe that most white Americans feel culture-less. I've never heard anyone express that belief in my fifty years of living in the USA. I've known people who are interested in traveling to Europe, and I was interested in doing so myself, but it's never been to feel some sort of connection that they don't presently feel. Few are thinking, "Oh, I'm an American, that means I don't have roots, I'm missing some some vital connection, I must connect with my heritage." If a person was born in the USA and has lived all of his or her life in the USA, THAT is their heritage. It's a strong heritage and it's one to be proud of. I don't like hearing sentiments such as yours because it implies some sort of superiority of European countries to the USA and depicts Americans as some kind of yokels who aren't capable of creating a culture.