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The understanding of higher musical structures is not easily achievable. It takes a lot of sophisticated training to understand the modern art musical universe. That's why modern music is not easily accepted by wide audiences. Cage was sound experimenting more than composing, he was an important historical figure, but not even composers listen to his music often.

We can say that art, musical or pictoral, has two kinds of expression: the hieratic and the demotic. One is characterized by increasing complexity of order, the other a decreasing complexity. If we stretch the poles further, beyond the demotic there is the avant-garde and beyond the demotic there is propaganda. It probably is true that all great art is neither of these extremes, but mixture of the demotic and hieratic.

It takes a lot of sophisticated training to understand the modern art musical universe.

There is a nice piece by Ortega Y Gasset on this subject in The Dehumanization of Art:

Every work of art awakens different responses: some people like it, others do not; some like it less, others more. No principle is involved: the accident of our individual disposition will decide where we stand. But in the case of modern art the separation occurs on a deeper plane than the mere difference sin individual taste. It is not a matter of the majority of the public not liking the new work and the minority liking it. What happens is that the majority, the mass of the people, does not understand it.
In my opinion, the characteristic of contemporary art 'from the soiological point of view' is that it divides the public into these two classes of men: those who undertand it and those who do not. . .
Modern art, evidently, is not for everybody, as was Romantic art, but from the outset is aimed at a special, gifted minority. Hence the irritation it arouses in the majority. When someone does not like a work of art, but has understood it, he feels superior to it and has no room for irritation. But when distate arises from the fact of its not having been understood, then the spectator feels humiliated, with an obscure awareness of his inferiority for which he must compensate by an indignant assertion of himself.

Cage was a charlatan who proved once again that some things are so stupid only intellectuals believe them. My belief is that Cage knew early on that he lacked any musical aptitude but like legions before wished to be famous. How then to gain fame? Why by concocting his "music" system and gaining the praise of all sorts of screwball avant-garde music critics who also wished to be famous. Cage, Schoenberg, and others like them are musical frauds and dead-ends like (c)rap "music".