I actually agree that this is currently a big problem. My group is set to reply-all, but often, topics are set to private-reply. In that case, as well as when someone purposely selects "private reply" in a reply-all (i.e., default) topic, you can't see the addressee when you reply.
This has resulted in numerous cases of private replies going to the wrong person. Some people don't realize that "private reply" means you're replying to the person whose post you are directly under, and mistakenly assume that their reply is going to the OP. Even if they do realize, some people goof and reply underneath the wrong message.
I strongly agree that adding the addressee would be a boon by reducing (if not entirely eliminating) this kind of error.
Messages are the sole opinion of the author, especially the fishy ones.