We'd have to do a study to know for sure, but as a North American having lived in Western Europe for several years now, I think you are massively overestimating the importance of the US in Europe or the world. Most people here know next to nothing about the US or the anglosphere, except for some stereotypes and exported cultural artefacts.
They know about as much about the US as the average American does about Germany or how to speak German, which is basically nothing.
One has to remember, English is a business tool here, the majority cannot speak English fluently, and they do not use it in their free time, or if they do it is to watch US TV shows or movies, not read American literature. Add to that, that more recently, a lot of the people I meet openly hate the US.
Most Americans who visit only interact with the segment of population which can speak English, not with the majority of locals who can't.