Yes, the USA is a master of making itself seem much more powerful and important than it really is, and what do news outlets love more than painting the devil onto the walls? Denmark living in the USA’s pocket doesn’t help much either.
At this point I wouldn’t be surprised if more Europeans know the presidents of China, Russia, and the USA than know the name of our own European prime minister, which would be pretty sad if actually true.
Of course it’s important to know what other countries are up to, and the EU is currently reliant on the USA for conflict handling (please make a joint European army), but unless you plan to intervene then I see no reason to fanatically follow their politics. Just tell me whether we’ll have to deal with some ancient inept dude, or another ancient inept dude who has managed to weaponize incompetence.