Frank Kogan

Actually, I'd say that "we are famous for not having talents" could possibly be a point of pride, in that there are always people bemoaning how idol groups often can get away with little to no performance talent or releasing bad music because they're funny in variety. That 4minute is famous for not doing imitations implies that they don't have to stoop to that level, that they can stand on their performance talent and good music alone, being "more legitimate" artists. Some people praise 2NE1 for being notoriously awkward on variety, (and thus rarely doing variety appearances) taking it as evidence that they are more sincere and less fake than their peers, who play the "image first, music not so important" game.

There are certainly people who dislike Hyuna's brand of erotic cuteness, usually those who associate cuteness with youth, and thus find erotic-cute to be a wrongful sexualisation of the underage. And I do feel like there is a little bit of that in general backlash against Hyuna's sexiness, due to her babyface. (rivals Selena Gomez's) There's also general outcry against sexualisation of the young because she is the youngest in 4minute. (Conspiracy gossip was that she was a little too spicy for the Wonder Girls.)
These are more an extension of the debate on aegyo, however, and usually dorky behavior is not included under the conduct frowned upon. As askbask pointed out with his links, "dorky" might well be high praise for any idol.

Have performers succeeded by challenging audiences?
I don't have enough experience with the rest of Kpop to say. From this, it seems that anyone who achieves mainstream success does play the game at least a little, especially for squeaky-clean commercial endorsements.

This is further complicated in that fans' devotion becomes so complete that, arguably, challenging actions that are accepted by their fans cease to be challenging, because the fans accept both challenging and not in exactly the same way. They paint over all actions with blind adoration, and revel in that adoration, not thinking on any challenges that might be present. askbask mentioned the Jung sisters' aloof images, and some of their fans find it a point of appeal, but not in the sense of masochism. Rather, it's affection from seeing the contrast to when they do let their guards down, taking satisfaction in knowing that they have called their idols' bluff, knowing that they can actually be just as dorky as the rest at times. Like falling for the bad boy because you think that you've seen through their tough and gruff exterior to their mushy inside.
Instances where the challenge is actually acknowledged have always become scandals where the artist is painted with the "diva" brush, seen as ungrateful to their fans, and well, Kim Kwang Soo attempted to do that to Hwayoung because the consequences of the "diva" image are so harsh in Kpop. So idols are always, always, always sure to reassure the fans that any challenging actions are merely part of their concepts, fierce or sexy or what have you. Thus fans are free to dismiss any challenging behavior not as an inherent personality trait of the idol, but as more evidence of their skill in being able to portray these wide varieties of concepts. G-Dragon smashing a guitar on stage loses any incendiary meaning, especially when he frames it as purely performance later. Fans: "Awww, he was embarrassed! How cute!"