Frankly I don’t think that Europe has put out much in the way of “great music” lately such as the classical and romantic era composers that you mentioned. The fact of the matter is that most of the “music” that is “popular” is crap no matter where in the world it was produced.
That being said, America gave the world Swing music, the Blues and Jazz. And George Gershwin was an America Composer who probably was the equal of many of the classical greats. I also believe that John Williams should be included in that category.
Below is a link to a Jazz standard from the late 1950’s which shows that not all great music is composed with quills and pens and some music just comes from the heart:
Take Five:
https://www.youtube.com/watch?v=o2In5a9LDNg
I love this.