The idea that the schools are encouraging the students to compete with the original authors of works taught in the classroom is fanciful by the meaning that courts usually apply to competition. Your example is different from this case in which Ross wanted to compete in the same market against West offering a similar service at a lower price. Another reason that the schools get a carveout is because it would make most education impractical without each school obtaining special licenses for public performance for every work referenced in the classroom.
But maybe that also provokes the question as to if schools really deserve that kind of sweetheart treatment (a massive indirect subsidy), or does it over-privileges formal schools relative to the commons at large?