I heard a lot of these reincarnation stories while I was growing up too. Personally, I always believe that even if reincarnation were possible, it wouldn't be fun since one may not have any memories of the previous life.
And if this is true, it means that we all are on auto-repeat and might have lived several lives already. Well, like you said, "If wishes were horses..."

Thank you for sharing your thoughts on reincarnation.