America cannot be compared with the EU, firstly it was appropriated by Europeans and when they travelled there to make their new lives, that decision was absolute, they could not stay rooted to "the old country" in the same way as it is possible to now with the tools at our disposal such as the internet. So whilst they retained elements of where they came from food, language, en masse they were signing up to collective new ethos and they were doing that of their own volition rather than having it foisted upon them, with the exception of black slaves who being snatched from whence they came had no choice in anything.
As for "Little Englanders"a big bollocks to that! I have quite a few cousins in France, who are a quarter English as we share the same grandma, they are far more entrenched in their Frenchness and everything French than I have ever been in being part English, born and bred here, whether they are typical I couldn't say, a couple of them hate seeing French culture being diluted, my perception that is not the case here, or at least around London where I live. Although it didn't preclude one of them wanting to come and live here in London with our grandparents when he thought he might be drafted into the Algerian war when he was a young man, although happily for him that finished around the time that might have been a possibility.
However, from what I read there is very little appetite for federalism in Europe, indeed where other parts of family emanate from Sicily, they don't even see themselves as anything to do with the Northern part of Italy, the mindset is regional. Well a bit like our friend north of the border who doesn't see themselves as being part of Britain.
As the French are prone to say "Vive La Difference" it's what makes us all special! not being some unwieldy homogeneous mass.