I would maintain that most of the archetypal American foods still have strong ties to all our various mother countries. While we tend to do more "hot smoking", smoking meat is a thoroughly European custom, prevalent particularly in northern Europe (more often cured smoked meats and fish).
"French" fries are Belgian!
And how funny that two of the most classic "American" dishes are named after cities from the Old World...Hamburger, Wiener, Frankfurter. American food is just fusion! From tacos to spaghetti to hot dogs to lager beer, we take things from the Old World and do them in slightly different ways...they become almost indistinguishable because of new ingredients and cultures over here, but the lineage is still there. Look at the microbrew renaissance. We finally stopped doing knock-off beers of the Germans after a century or so, and decided we wanted to brew unique stuff, like......UK Pale Ale, UK ESB, UK Porter, Stout, etc...
Sure, anything domestically brewed labelled "ESB" doesn't taste anything like British beer, but we naturally are in to taking old influences as starting points and tweaking them. We're a young country still, we can do that!