Except Dany never actually was a "super competent girl genius". That's the whole point---she looked incredibly competent in the first three books simply because all of her adversaries were supremely incompetent. The tactics that seemed so brilliant at first---cheating the Astapori out of an Unsullied army and then slaughtering the Astapori nobility, "Dracarys!", freeing all the slaves so as to deprive the slavers of their armies---were "brilliant" only in the short term. ADWD is merely the point at which the inevitable consequences of Dany's actions finally started catching up with her: she now has a rather well-deserved reputation for treachery, so her word is mud and nobody believes she genuinely wants peace; setting an emissary's tokar on fire just added to her terrible reputation, cause really, what kind of person attacks an envoy?; and the same actions that allowed her to neutralize the slave armies of Astapor and Yunkai led to a situation where she's stuck with tens of thousands of useless hangers-on whom she cannot feed or protect from disease; etc., etc.
All of our other POVs are centered in Westeros, so we got multiple viewpoints on characters and groups of characters. With Dany, we spent the first three (and most of the fifth) books only seeing events from her perspective, so of course she was going to be portrayed in a positive light. But if we look at Dany's entire arc with a critical eye, certain discrepancies pop up even at the very beginning: for example, was she really as well-integrated into the Dothraki, and as well-respected by them, as she believed? Were her "great military victories" in Slaver's Bay a result of her natural military cunning, as Dany and her hangers-on believed, or were they the result of incompetent adversaries coupled with Dany's own appalling lack of foresight and judgment, as ADWD seems to show? Is being a Targaryen the answer to Dany's problems, or is it the root of those problems? Is Dany really "a dragon", as she desperately wants to believe, or is she merely an ordinary person who performed a magic ritual and started buying into her idiot brother's delusions?
Tywin, Tyrion, Littlefinger, Varys, etc. have all done some truly spectacularly idiotic things, things which either led to their downfall or seem poised to lead to their downfall in the future. The idea that they've been portrayed as naturally "smarter" than Dany seems bizarre. Dany has never been taught how to rule, has never had a mentor to teach her to rule (the only advisor she ever had who ruled anything in his life was Jorah, whom she sent away right before declaring herself Queen of Meereen), and she hasn't even had the opportunity of watching another ruler (save Drogo, who wasn't exactly a good role model here). She's trying to rule a city when she 1) has never ruled anything in her life, 2) was never taught how to rule anything in her life, 3) has nobody around her who's ever ruled anything in their lives, and 4) has a superiority complex that's been consistently fed and ennabled by literally everyone around her. The idea that it's her gender that's the problem is, to me, kind of absurd.
The whole point is that anyone who was raised in exile by a delusional narcissist, who was never taught how to rule or play any political game, who believes her gut reaction is always the correct reaction because nobody ever calls her on her BS, and who surrounds herself with yes-men whose goals aren't always in line with hers, isn't just naturally going to succeed in ruling anything. She's not learning from her mistakes, not because she's somehow naturally stupid, but because she has nobody around her who's willing or able to point out those mistakes. If she had people like Donal Noye, Aemon Targaryen, Jeor Mormont, Mance Rayder, even freaking Ygritte---people to smack her down when she needed it---I doubt she'd be in the situation she's now in. But a major reason why she doesn't have these kinds of people is because you can't consider yourself the uber-special "blood of the dragon" and be willing to get smacked down by non-dragons.