To me American Exceptionalism can be distilled down to "We don't need no stinkin'..." [fill in the blank].
Certain segments of American society believe that our way is the only way and refuse to even study other countries' ways of doing things...not to mimic them, but to take the good things about them and adapt them to the American way of life.
But, no. We can't have Nice Things. We're Americans, dammit!
Another term for that is "self-defeating pigheadedness," IMO.
That's one way to look at it. You might also acknowledge that people simply have different ideas about what Nice Things means. One of the benefits of being a nation built on waves of immigrants is that it forced us to face that fact regularly and, perhaps even by necessity, learn to accommodate it.