We're social animals. I've never had reiki but I have spent some time in hospitals. You know what you NEVER get in a hospital? Someone touching you in a way that isn't associated with a (usually painful) medical procedure. There is literally no aspect of hospital life that accommodates human sociality. So the idea that someone comes in to your hospital room and touches you gently and that makes you feel better? OF COURSE it makes you feel better. In the same way that therapy dogs make you feel better. It's social touch. It's pleasant. It addresses an incredibly deep-seated need in the human psyche, one that if it is not met eventually results in - if nothing else - significant mental health issues.
So it seems to me that the right scientific study to do here is not whether reiki improves on (say) chemotherapy outcomes; it's whether any sort of touch therapy, including therapy animals or just regular hugs from family, results in improved outcomes.