When people use the phrase "Polish American" or Irish American they are saying where they're ancestors came from and not that they themselves are Polish. My wife's grandparents, came from Poland to the US, now ask my wife her nationality and I'll tell you now, she will say she's American.
Not Polish American or any other kind of American, she'll tell you American. Millions of Americans are exactly the same and won't mention heritage until asked usually.
About the only time you'll see or hear people going on about heritage is at festivals type days out.
You're wrong about that as well. Put it this way, my drive into town is 100 miles there and back, on that journey I might count three or four flags outside of homes. About the only time you'll see flags flying from lots of homes is during Memorial Day and Independence day and they are taken down and stored after use.
P.S. I don't have to stick my head anywhere mate, unlike you I know what I'm on about.