I had a similar reaction to "Assassin's Apprentice" by Robin Hobb; although not as perfect as Kvothe, her Fitz has all the possible talents in one place, from the Wit to the Skill etc. On the other hand, Hobb's Liveship Traders amazed me with the complexity of the story, as well as the beautifully designed characters (nearly none was a two-dimensional caricature but a real human being with feelings and motivations) -- it was like the reading a completely different author.
The point is made many times that he is an unreliable narrator, and that this is a self-mythologising, which is part of why I like it.
They are exceptional by design. If they weren't amazing swordsmen, or magic users, or highly intelligent, or highly determined, they'd be dying at the first hurdle in the story - which is equally ridiculous for a novel. The alternative for underpowered fantasy characters is either a non-perilous story or a lot of "deus ex machina" moments where the character survives by "random" chance. Neither of which are particularly interesting.
Narrative imperative does have some demands on story characters, but it's all down to the quality of the writing as to whether you can suspend your disbelief.
Take Frodo Baggins, Thomas Covenant, Malta Vestrit, Jon Snow, Miles Vorkosigan, Sherlock Holmes or any of the countless prominent characters from fiction of any genre -- they are all quite exceptional, but also significantly flawed in one or many ways. I didn't see any prominent flaws in Kvothe, which made him really boring and uninteresting; now, as someone else mentioned, he is an unreliable narrator of his own life story, and it is quite possible that in later books it will turn out that a lot if it was a lie and his flaws will be revealed, but by then I have long lost my interest and I don't think I'll ever get that far. I do enjoy a good twist in the story, but the story up to that point needs to be interesting on its own; Usual Suspects wouldn't work at all if Verbal Kint was a flawless character.
I just noticed though, as I'm writing this reply, that most of these flaws come out in the second book, not the first. Maybe you need to stick with the series a bit more before making up your mind.
That's why I found it quite frustrating reading the 2nd book, as the present/future feels like where the "real" story lies, but it made absolutely no advancement in that direction. So I definitely agree with you there, the focus on the super-powered young Kvothe does detract from the main story as I see it.
I will have to try Liveship traders