I'm hardly a philosopher, but I know a little about postmodernism etc, and feel comfortable discussing the topic.
While perhaps the postmodern idea that posits high and low culture as a false dichotomy isn't entirely true, I'm not sure that I agree with the black-and-white idea of pieces of art fitting into categories a & b either. This is probably because I hang around experimental and avant guard art scenes quite a bit, where high and low (good movie) are seemingly largely defined by audience rather than by merit. A few examples:
Is Sunn O))) high culture because their music structurally resembles works by a number of minimalist composers like Eliane Randigue, or are they low culture because they do this within the framework of heavy metal? Are Swans high culture because of their playfulness with form and convention and their apparent difficulty, or are they low culture because they're a rock band? Are Frank Zappa and Captain Beefheart high culture because of the avant-jazz elements of their music, or low culture because of the rock and blues elements? Is jazz itself high culture because of its structural complexity, or low culture because of its roots in popular music?
Of course, this continues to rap. Is Milo high culture because of his syntactical complexity, philosophical themes and constant references to literary fiction, or is he low culture because he's a rapper? What makes Milo different from Thomas Pynchon or James Joyce? What about Sole? Is Flying Lotus high culture because of his recent focus on frenetic, complex compositions, or low culture because he doesn't posit himself as a composer? Is Death Grips high culture because of the experimentation and incredible technical proficiency, or low culture because of the yelling? Examples continue, but I think I've made my point.
If it is the case, it's unfortunate that there is less of a focus on higher forms of culture, but it makes little sense to blame it on rap music.
Firstly, because you've not explained why hip hop is less likely to direct youth towards "high culture". Without putting words in your mouth, I'd guess that it has something to do with rap's lack of focus on melody. I've heard this argument before, but I find it silly to place one part of composition over another. Also, there's an awful lot of jazz that shares hip hop's focus on percussion and rhythm over melody. Check out this: https://www.youtube.com/watch?v=0wgA9L5TN5M. Also also, rap's focus on lyricism and poetry seems to be as likely to direct attention towards literature as anything else. Check out the beat poem that Kendrick Lamar (who is very popular) employs here: https://www.youtube.com/watch?v=_ZTYgq4EoRo.
Secondly, there are other factors that ought to be taken into account w/r/t the (allegedly) decreasing focus on high-art. At least where I live (and go to school), funding for the arts in school has been almost cut out for years. Art classes (be they music or visual arts or film) are neither required nor encouraged. Until the very end of secondary school, serious literature is not read in English classes, instead focusing on (in my opinion) young adult schlock like Divergent. This year we read Macbeth (which was very good by the way), but even that isn't mandatory for teachers and seems to be the exception. There are all problems that I think ought to be fixed, and ones that seem to contribute to the sort of problem you're talking about far more than a little Wu-Tang.