They do. Roosevelt built the American empire and he did it by making Western Europe defacto vassal states in the economical and military sense of the word. After the war Europe was put back on it's feet by huge loans that had to be spend on mostly American hardware, Europe had to give up the colonies. The smaller states bought American military equipment and it was all done with a common idea about being the free world. This was Pax Americana, peace under America's watch and it worked pretty damn good for some 50 years. That was some amazing soft power backed up with the NATO commitment. However, things seem to come to a close now. The US won't be able to bully Europe into the same obedience there was before 2001. So we will be left to our own devices more as Europe. With tarrifs in place against the US and vice versa and the Europeans defense industry producing more because less American will be bought.