The thing is, the Justice League and the Avengers aren't (usually) considered US teams, but rather have global scope. It's true that most of their members are US citizens, but they operate on the planetary level, and often beyond.
Then you have teams directly created by the UN or otherwise by the international community, who are full of international heroes, some of them being themed after national myths or lore, or even the mythological beings themselves. Things like the Global Guardians or the Ultramarine Corps (which is actually an official US team, but the membership is international, because they're supposed to match the Justice League's global scope).
Strictly national teams don't usually have outliers like that, and whenever there's a strictly US team, they're either state-themed or strongly themed after the Armed Forces.
TL;DR: the JL and the Avengers are global teams, despite the US being overrepresented in their rosters. Official national teams, even the US ones, tend to stick to National themes.