I find your comparison not so convincing. While there is some common misidentification between the EU and Europe, I’ve never heard anyone in the world refer to “America” in a way that was not for the United States.
And in French the inhabitants of "les Etats-Unis" are "Etats-uniens". I've taken the habit of referring to them as USAians, which often gets negative reactionsand remains rare - but I find it is the most accurate demonym and I'll keep pushing it.
I look forward to the world inventing demonyms for the citizens of the European Union, because at least it will mean that our emerging national body is getting mindshare !
USA is a country and EU is not
That ambiguity disappears if you call it "the Americas", but many places see America as one continent (including Latin America, parts of Europe and the Olympic flag)
One of the most famous soccer teams in Mexico is even called “Club América”, obviously this doesn’t refer to the US.
Which is, of course, true; however, in English conversation, it's often nothing more than pedantry. In Spanish it makes more sense, since there is a separate demonym for a US person that doesn't co-opt the term "American."
Outside of Romance language speakers born on the American continents, I agree that everyone seems fine calling US-born persons "Americans" without much confusion nor gnashing of teeth.
Which is all kinds of weird because - what about Mexico and Canada? And what about the ‘United states’ part?
It’s just to disambiguate from ‘Americano’ as in what others in South America sometimes use to refer to latin Americans and as a little bit of a FU to the USA, hahah.
In French, people from the Americas are américains. This includes, say québecois and Brazilians. When context matters, people from the US are états-uniens.
The point is that nobody would object if you refer to someone from anywhere else in the Americas as américain. Like my lab mate from Buenos Aires or friends from Montréal. And we’re definitely not in Haiti.