There are two parts to this. One is (cold war) propaganda where there is a somewhat vague feeling that the USA has to a greater or lesser extent a set of shared (western) values and aligning ourselves next to them is probably in our own long term interest given the uncertainty that a world dominated by Russia and now China, or, gasp, religion (yes, I know) might bring. The second is aspirational - generations of Europeans and probably other countries too have looked to the USA (and Canada, Australia, etc.) as a way of improving their lot through emigration.

For all it's flaws, I loved my time in the USA and appreciate the people and a lot of what it stands for. Despite of all the imperial crap that comes out of Washington D.C. the USA still represents a sense of hope for a lot of people.

America still has a lot to offer the world. It's role in the world is greater than Holywood or the government. Merry Xmas.