Native to the American musical impulse is the urge to improvise; all kinds of musics attest to that from Native American to jazz. Does this make the study of classical music irrelevant to American kids?
It shouldn't. Consider how important improvisation was throughout the history of what we call classical music. Why aren't we comfortable letting our kids improv(is)e on music they know from reading? What is so sacrosanct about the printed text?
Mind you, no one is fussier than I am about reading accurately and sticking to the text. But there is sticking and there is sticking. When music is all repetition--i.e., when timing and balance are rigidly pre-figured, there is no traction in the player's or in the listener's ear-brain.
I hear it all too often in the concert hall and see no reason why I should allow my students to think that that is music.