I think when we travel abroad, we're aware everyone can tell we're Americans without our having to say so :-)
> I always wondered why is that so? Do they assume people around the world know their geography? Do they don't learn at least a little about other countries at school?
It's habit. It's how we talk to one another about where we're from—major city, or nearest major city. Aside from a few states where people like to lead with that (mostly Texas and California—meanwhile, if someone says "New York", they probably mean the city; there's a little easy-to-miss comic jab about this in the show Archer, where Archer a couple times corrects someone who says "New York City" with "you can just say New York", as the latter usage reads "higher" in a social-class sense). It's a consequence of our largely-homogenous culture being spread over such a huge land area, I think.
Recall, again, that we generally have way less experience talking to people who live in other countries, on account of how very far we have to travel to encounter many such people—and even then it's mainly Canadians, who can and do sometimes pass for American pretty well (we're much worse at passing as Canadian) and Mexicans, those being the only two countries that share a land border with us. 99.9% of the time when we're telling someone where we're from, it's someone who is familiar with US geography.
Besides, "American" doesn't narrow things down very much. It'd be like someone from Germany leading with "Europe" when describing where they're from. Right, I guessed that already—but where? Germany? Austria? Switzerland? Belgium? Our nationality is far less specific, geographically, than those in Europe.
> But don't they generally feel curious about other cultures, reading foreign original works, or simply getting a grasp on how other languages express ideas?
Sure, but it's a big commitment to both learn a language and keep up that skill, and it mostly has to be maintained kind-of "artificially", for Americans. Conversational skills and accent in particular can be very difficult to maintain.
Americans remain strong aspirational speakers of second languages, it should be noted—Spanish and sometimes a few other languages (French is common, Chinese increasingly so, others like German or Italian sometimes) are taught, to some degree, to nearly all our kids, but it's hard to even find good teachers because there's just no culture in which to keep up those skills, so a lot of the time those classes are taught by people who aren't good speakers (let alone native) themselves. The kids, for their part, promptly forget everything except a phrase or two, since they never use the language outside class, and even the ones who try to go farther find it both practically difficult and, lacking much extrinsic motivation or a kind of natural need, discouraging.
> reading foreign original works
I mean... very little reading happens these days, period, aside from trash-tier online reading, romance novels, and self-help books. At least in America. We're far removed from a time when "author" could practically be counted a blue-collar profession, there was so much demand for fiction. Among the same groups of people in which reading remains semi-common, you're likely to find folks trying desperately to hold onto their grasp of one or more major literary foreign languages (and mostly failing at it).
[EDIT] Actually, now that I think about it, you may also be seeing some class bias—Americans who can travel abroad are more likely to have at least some of their culture and norms influenced by the set of people who think in cities (if not more specific!) everywhere—they don't visit France, they visit Nice, they don't visit Italy, they visit Milan, they don't have a modest apartment in America or even New York (City) but Manhattan, and so on.