Why can John the Savage not exist in the world of Brave New World?
Let us just think about John and how he "fits in" to the world of the future that Huxley presents us with. Throughout the novel he represents a character who has not been conditioned to unthinkingly accept the new society we are presented with, and thus he acts as a commentary on it. In addition, his belief and acceptance of the "old ways" of the world, which have largely been eradicated, make him singularly unfit to belong in this new world. In particular, his devotion to Shakespeare leads him to completely misjudge so much of reality in this brave new world.
A classic example is based on Lenina and his feelings for her. John's relationship with Lenina, in terms of his problems with trying to work out what he actually thinks about her and his eventual suicide seem to come straight out of a Shakespearian play. John lives life based on his emotions and looks at himself in a way that stands in bleak contrast to a world where emotions have been devalued and people no longer examine themselves.
Thus it is that John's allusion to Miranda in The Tempest to describe this "brave new world" indicates why he cannot exist in this future dystopia. As he understands how this world operates he comes to see that he is not able to live in it, as his response to his mother's death shows, to give one example. Note how the nurse responds to John's show of grief at his mother's death:
The nurse stood irresolute, looking now at the kneeling figure by the bed (the scandalous exhibition!) and now (poor children!) at the twins who had stopped their hunting of the zipper and were staring from the other end of the ward, staring with all their eyes and nostrils at the shocking scene that was being enacted round Bed 20.
Grief is not an acceptable human emotion, yet it comes spontaneously from within John, reflecting his identity and values. His final participation in the orgy and his death at his own hand seems to represent the conflict between his own core values and the values that are forced upon him. With this inner conflict, John could never have lasted in this new world. He sees things too differently.