In my book, Ad Infinitum, reincarnation is a means to an end, a tool used by generations of humanity to pass along knowledge through the commonality of our sentience, which binds all of the higher orders of life. We are all of us made from the same cosmic and multi-universal material and we all resonate with our own unique signature, a bioelectric wavelength as unique as our DNA that literally pulses with life. It is the Eternal Resonance.
Those wavelengths, once accessed, transcend spirituality and connect us through as pure a natural process as could possibly exist. So, the passing on of those signatures through time by the reincarnation of what we, for lack of a better term, call souls, is a natural thing that happens regardless of our intention or beliefs.
It isn't spirituality; it's life.