Old guy, I think you misunderstood me to a certain degree and as for having my judgement "clouded", not really, it's not a matter of who defeated who which makes me say this, especially when Yukari is one of my favorite character in the series. After all, by that logic, one could say that some people considers the Watatsuki sisters to be Mary Sues because Yorihime curbstomped a bunch of popular characters. I'm not sure if she isn't infallible since, again, she typically, if not always succeeds at what she's trying to do and do whatever she feels like.
The thing is, one could say she's a Mary Tzu which may have some merit (again, I said she may be the closest we have as a Mary Sue, not that she flat out is one) but all her antics indeed comes at a price seeing how most people tolerates her at best and many do not trust her to the point they'd rather not interact with her, almost as if they had to deal with the devil itself. On the other hand, if we start to overanalyze the character, a thing with Yukari is that, does she even care about that?
If she does, it sort of make her a tragic character who does her duty regardless of the consequences. After all, she's most likely not emotionless. She's not without friends and while there were no consequences for what she's trying to do, Kasen's words seemed to actually affect her enough to leave her speechless for a moment. However, if she doesn't care then, as TresserT said, we have a character who's ultimately not affected by her own flaws, thus making her capable of doing what she pleases, succeed all the time which might possibly result in a boring invincible hero/villain. Obviously I prefer to think it's at the very least not the latter.
As for the mouthpiece thing, yes, ZUN used other characters to do that but there are times where one can immediately figure out what's going on. That by itself isn't a bad thing. However, I feel earlier instances of this came off as overly preachy, if not pretentious at times. Personally, I feel he did a far, far better job later with SoPM and AFiEU compared to older instances of that which shows that his writing has been getting better. Case in point: Forbidden Scrollery.