I think there are two main issues.
Firstly, classical music is no longer the idiom to which children are likely to be exposed to; there are plenty of other forms out there. Can you imagine that Liszt would be as famous/notorious if he lived today? His agent would probably suggest an affair and urgh, a "crossover" album with, for example, J-Lo.
Secondly, art has historically shown a tendency to disappear up its own backside in the process of its evolution (in some cases, becoming embarrassingly self-referential). I'm sure that Jackson Pollock, Damien Hirst, etc are probably less likely to be appreciated by the general "uninformed" public than, for example, Rembrandt or Monet. It's probably a cheap analogy, but the same surely applies to any random modernist when put alongside Beethoven or Debussy?
This occurs because, as artists/composers are intellectually curious, the progressive ones do not wish to stand still, and seek to push the boundaries of their art form (I am certainly not arguing that this is a bad thing, btw). However, for those who are less "artistically educated" or whoever you wish to put it, perhaps it renders the end result less accessible? And music, like art, has reached such a point.. where modern classical music is inaccesible to many and the music of Beethoven, Bach etc is wrongly perceived as passé and redundant because the composers are dead?