To be fair, American culture is not homogeneous either. There are multiple cultures throughout the country. Whatever version of thinking you're talking about is likely has both supporters and detractors here.
The idea that their army is the coolest and will save us from aliens, that their bilionaires (oligarchs) are secretly superheroes, that foreign leaders are crooks secretly plotting to conquer the world and so on.
These are Projections
Nothing more American than this example of how an oft-derided-in-the-rest-of-the-US bunch of coastal Hollywood elites constantly put out a bunch of movies glorifying guns, violence, capitalism, and the USA.
Also it's not just about this over-the-top movies that are completely out of touch with reality. Often the propaganda is subtle and even unintentional, made by victims of propaganda themselves.
There have been occasional British TV shows/movies with this premise as well. That's not American culture, that's "what would happen if aliens invaded and we make a movie about that" culture.
The reason you think it's American is that only the Americans seem to make sci-fi these days. I don't know if that's budget or culture or what. On HN we talk a lot about how impoverished the Euro tech scene is vs the USA but it's not just tech. Italians use a lot of English words because the Euro movie/TV scene is also out to lunch. What was the last mega-franchise that came out of Europe? Probably Harry Potter? So, Europe but not EU. And Harry Potter was created in the UK but actually brought to worldwide attention thanks to investment by ... Americans.
My guess is it's due to the dominance of government funded media firms. What's the best known European sci-fi franchise? Dr Who? A relic that dates to the 50s. The BBC lost interest in sci fi and fantasy a long time ago. Too expensive, only popular with unpopular demographics. Far better to make yet another 1800s period drama.