Even in the European/western cultures, very few understand European classical music. It's "art" music and the majority of people, including instrumentalists and singers, are drawn to it for it's aural aesthetics, not it's ability to communicate. Thus, it's rare for even the very capable of musicians to truly understand the meaning of the notes. They can sound very good, capable of fooling an entire audience, but what's really important is that they communicated the ideas in the appropriate manner. Sometimes that will sound ugly, but only true musicians will understand that and have the nerve to express it with its full ugliness.
I don't think saying this kind of music is rigid is appropriate. That would be like saying Shakespeare or Tolstoy is rigid. Anyone can recite the words of Shakespeare, but to say them in a manner that appears as if he was expressing it for himself, because that is what he is feeling, is a difficult art to achieve. This is the difference between a musician and an instrumentalist/singer. There are too many of the latter.