Once you email someone, the mail should also show up in your inbox to maintain continuity of the thread. It doesn't need to be copied there, it just needs to be shown. It isn't helpful to have to go looking into the sent folder and connecting which email was sent after what reply. 

I think gmail follows this paradigm, it adds your reply to the thread too hence maintaining the continuity of the thread and making it easier to follow. A marker could mark the message as "sent".