For the record I am not proposing that kids stop playing sports, only that these should be handled by community sports clubs rather than educational facilities. High school sports in particular, in my view, promote a toxic variety of tribalism (look at the reaction around Steubenville) and help to form a social elite both within and outside of the school environment which values said athletics while either disregarding or mocking intellectual pursuits and achievements.
If community teams replaced high school teams as the primary youth athletic organizations, a similar culture would grow around them as well.
Also, I doubt the existence of the teams themselves leads to their players being anti-intellectual. Stereotypical "dumb jocks" will exist regardless of whether they play sports at school or not. And, there are plenty of high school athletes (probably the majority in most schools, though maybe not in your experience) who don't fit that stereotype at all.