This implicates the brain and experience being genderless, which does not really seem to pass by today's understanding of it. But then again, the brain would probably also experience a very traumatic phase of body-adaption. There are many syndromes with people having strange feelings about the body they were born in, or missing parts of it; how awful would be to switch the whole body overnight and not having a long phase of adapting to it. Not sure if I would really call this elegant. But then again, body switching is quite common in SciFi, and those aspects are usually completely ignored.