Actually Conan didn't represent the stereotypes of "Unearthed Arcana" book for the most part. He's gone through many iterations, but the basic point of Conan is that people tend to THINK he's a Barbarian, and think that he's stupid, and while he holds to some of the Spiritual beliefs (Crom) he's actually VERY smart, and VERY well educated as well as having received formal training in combat aside from his native barbarian might. Indeed having read a lot of the old stories one key element of Conan seems to be him routinely running into something he can't just beat down, and then winning anyway because he's very smart (and by this I don't mean just cunning) and turning the tables on his enemy. In simple terms I think he was the quintessential "fighter". The various "picts" that appeared in the stories were Barbarians, and I believe existed in part to make a counterpoint to Conan, and even what the other Cimmerians (when they showed up) actually were. Part of the point being the ignorance of more civilized people like the Aquilonians.
THAT said, I tend to agree that fantasy stereotypes exist for a reason. However I will also say that it does wind up making games where characters seem like special olympians, everyone being unusually brute in one area, but totally deficient in everything else. That can be a neat concept, and works for certain kinds of RPGs, but I do not think that it's strictly speaking nessicary... although admittedly it DOES make it much easier for the GM, especially if they are inexperienced.
I have on occasion played various RPGs that didn't use those kinds of conventions. Taking a more fantasy-novel type track, where pretty much all of the PCs are pretty uber, even if they have their own specialties. Everyone winds up being fairly capable of surviving on their own, though the combined power of the characters acting in concert is far greater than they are apart. Things like White Wolf's "Exalted", point based systems like "GURPS", and even things like "Ars Magica" can all fit this definition.
Of course when your dealing with a group like that the GM has to provide a narrative to keep them together for the ease of running the game. You'll notice that in most fantasy novels, where everyone is pretty cool, the entire group does not stay together all the time. Indeed they wind up frequently pursueing the same goal, but operating in vastly differant areas and only behaving like a "party" in very specific situations. Easy to write, not so easy to GM.
On a final note, I think the quintessential wizard garb came from descriptions of magi through the years. I seem to remember once reading a long description about how one went about making a robe for a white wizard in Soloman's court which involved some ridiculous requirements if I remember going down to the thread and the type of cloth used. Not to mention the fact that "wizards" used to oftentimes be astrologers/astronomers and fortune tellers as well.
To be brutally honest the idea of wizards being old men with flowing beards and such who dress like that is silly, but mostly when viewed in the guise of a level 1 mage who might be able to light a candle. Truthfully when portrayed artfully the quintessential image of the wizard can be quite mighty seeming, I'd imagine some dude hold enough to have a nose and beard like that has been casting spells for a LONG time and would probably be into what the D&D rules would call the epic levels.
Simply put if your a kid just out of apprenticeship, who can toss his first sleep spell, yeah well.. normal clothing or more modest robes are for you. On the other hand if your the guy who has the huge magical library full of artifacts oftentimes in the backround of that quintessential wizard... well at that point your out to cut a certain image. The celestrial imagery probably says a lot about what your about, especially if astronomy/astrology plays some kind of role in your powers.