I don't know, I kind of have mixed feelings about adding another stream. I'd probably find stdinfo and stdwarn useful. But it's a slippery slope to duplicating the features of a full logging system; you might add stdinfo, stdwarn, stdfine, stdfiner, stdfinest, stdconfig, std$custom, etc. etc.
One nice thing about having only stdout and stderr is it pushes you to ask: "Is this piece of information actually necessary to display to the user or should it just be logged to a file somewhere?" I'm not sure everyone really asks that though. Every time someone shoves a bunch of needless information to stderr "just in case" is a time I have to 2> /dev/null. (At least the useless stuff is often in stderr so I don't have to grep it out of stdout.)
I almost think we need another output stream for something that's neither an error nor output of the program.