And it follows from this as night follows on day, that if you harm any one of those little bits of you that have a function, then you are harming a mechanism whose function is to help you to reproduce, and so you are harming your own ability to reproduce (to the extent that those mechanisms still function in your generation and are not mere functionless leftovers of an earlier generation).

I don't think that argument works given the fact that evolution never looks forward. It doesn't ask (even metaphorically) if some bodily feature or desire will continue to serve reproduction in the future. So we could easily wind up caring about goals that no longer serve reproduction. (ETA: This requires our environment to have changed faster than evolution could keep up, which however seems clearly true to some degree.) Calling them "functionless" would just beg the question.