I asked this question earlier today, and was informed that the envelope that lights up next to the login name seems now to have nothing to do with replies. Evidently, correct me if I'm wrong, the only things that envelope lights up for nowadays (according to Jarrod Dixon here) is "when [I] have edits on [my] posts or edits on questions [I've] favorited (if [I] haven't disabled favorite notifications in [my] preferences)".
Given that info, why does the envelope say "you have no new replies" when you hover over it? That gives me the wrong impression immediately about what that envelope's function is.
I would suggest that the verbiage be changed to "you have no new activity" when there is nothing of note, and when something you care about occurs, then the message could convey "your post was edited" or "your favorites have new activity", something along those lines. In that case, then the only purpose the envelope would serve would be a quick link to your recent activity.
Perhaps these would better be cataloged in the inbox as edit or activity types of messages (e.g., edit on Unclear Question, and activity on My Favorite Question).
Edit 1: changed "you have no new notifications" to "you have no new activity". This seems to jibe more with the reporting provided when the envelope is clicked.