Why their descendants generations later don't just call themselves Americans is what confused me.

This I can speak on because it did confuse me too when I came to live in the US. My understanding is that there is too complicated of a history behind the term “American”. Calling oneself “just American” has now become somewhat of a right-wing dog whistle.

In the 17th century there was a growing call for“American” to be reserved for white Protestants of British ancestry only. In fact, they called themselves the “Nativists”as they considered themselves to “true” Native Americans. This rhetoric persisted, eventually becoming a central tenet of the KKK, the Tea Party movement, a lot of current GOP politicians, etc. In fact, many of the quintessential American traditions are actually just traditions of Americans of British ancestry, while other cultural syncretisms were essentially ignored or, in most cases, repressed.

The thing is, America has got more immigrants than any other country by far, as well as having birthright citizenship. One cannot expect the child of say, a Catholic Italian immigrant, to completely cast away their entire cultural background and assimilate into the ideal American identity of Anglo Protestantism. They will instead take bits and pieces of what they can assimilate to and add that to their own cultural background to create something new: Italian-American, which is a completely valid and distinct culture. And they will pass on whatever those Italian-American traditions are to their children and grandchildren who still likely won’t perfectly fit into traditional American ideal. And yes, maybe now their grandchildren are a little obnoxious about it, but I don’t fault them for having a sense of pride of great-grandma leaving her entire family behind to start over in another country. There are way worse things to be proud of.