John Cage and the Question

This may not seem to be a blog post that is very related to what we are doing in DIY but I would disagree. First, it is slightly about John Cage, a composer not only mentioned in our text but one also respected among electro-acoustic composers and musicians. The second reason I would disagree with this opinion is that from this story there is a viewpoint or opinion that I think must be addressed and I am curious as to how others in this class might respond.
A friend of the family once told a story about his father had seen Cage perform in the 1960s. His father, he said, had attended the concert almost by accident; as he merely looked to find a show to bring a date to and a friend of his had offered his tickets to the concert. Without further thought, his father attended the show with his date and, needless to say, they were more than a bit a confused by the event. As they left, before his father could ask a question of the woman, she turned to him and said, "I think you are too weird for me and I think I am going home now." And she left. Simple as that. This friend's father was apt to remark then that Cage was forever "too weird" for any "normal people".
Who knows if the story is true (I would like to think it is) but the question is then is that true? Does Cage (or electro-acoustic music in general) appeal to only a certain aesthetic and does it alienate a more general audience? I like to think art tends to speak to something universally human but I do not have answers to these questions; and, therefore, I would like to hear anyone else's thoughts on the subject.