Could the music classes be made more difficult? Perhaps the composition and analysis part, but probably not the sight singing and keyboard labs. The keyboard labs, in particular, could be quite difficult for anyone but experienced pianists, even for the most basic of diatonic four-part harmonies. This is because multiple voices can move simultaneously, which requires a significant amount of coordination and technique. Poorly applied technique here, in an attempt to drink from the firehose, could result in injury. In fact, I'm just starting to learn how to play these types of harmonies, and I have to play them really slowly, using modified fingerings to preserve legato effect while maintaining comfort and safety.
Out of curiosity, I looked around juilliard a bit for some commentary on the courseload. I didn't find much (granted, I didn't look very hard). There are some posts on the auditions, understandably. Everyone has to audition to get into Juilliard for something specific (musical instrument, dance, etc.), whereas at MIT you apply to the school, and if accepted, you get to major in whatever you want, whenever you want. This is one of MIT's biggest selling points. However, I wonder sometimes if a more restrictive policy might prevent students from getting hosed, or at least give them a heads-up that they need extra background in certain areas before taking certain classes.
edit:: deleted broken link