Honestly, if he has all those things and he's so amazing as you say, why is he dead? Why did he let himself die, instead of countering Kakashi? Why didn't he just completely kill off Naruto and Sasuke when he had the chance? I can get why he didn't kill Naruto, since he gained that attachment to him. But I haven't seen anything from him truly that shows how truly amazing he is.
I mean Kakashi has seen his father commit suicide, the death of his two best friends (one by his own hands), and many, many other people/friends throughout a war. Sasuke saw the entire annihilation of his clan by the hands of his own brother. People attempted to kill Gaara many times, with his own father detesting him. And Itachi was the one having to kill his entire clan, then leave his village and live out the rest of his days as an S-rank criminal. Naruto had the nine-tailed fox in him so he was detested by the entire village almost his entire life. Literally no one liked him minus Iruka and the Third Hokage. So I'm easily going to disagree on Haku having the most tragic back story.
As for the observation/countering part, MANY ninja have been shown to have that attribute. Sasuke, Kakashi, Itachi, Nagato, and hell, even Naruto at this point. It's really not that special.
And again, with battle IQ, that's been shown by MANY characters. I'll give it that Haku is very, very skilled, but nothing that isn't really known by a good number of Chunnin level ninja.
I like Haku and admit that he is highly gifted and smart, but that's about it. Especially since he was a foe early on in the series where Kishi had to make things seem really out there and tough as far as the opponents went. Hell, Zabuza was shown to be this INSANELY strong foe, on of the most top-notch ninjas around. But since then we've seen more and more skilled enemies who are significantly better than him.
So I can't completely agree that Haku is the smartest there is. I'd probably, like almost everyone else, go with Shikamaru, his dad, and/or Itachi. Nonetheless, it's all just opinions and good OP. Not gonna flame you especially since I respect you for your admiration for Haku, despite all the shit you may get.