Not your garden-variety super hero
Ray Embrey (Jason Bateman): People don't like you, Hancock.
Hancock (Will Smith): Do I look like I care what people think?
"Put your John Hancock on this." How many times has someone used the signature figure of speech this way? Peter Berg's Hancock is also the real deal, a signature comic sci fi, super hero summer blockbuster unlike any other except Iron Man. Even Iron Man doesn't go far enough exploring the downside of heroism with the weaknesses of being human interfering with an ordered heroic world.
Will Smith as Hancock turns in a much more nuanced performance than his I am Legend loner because here he must turn around a public that sees Hancock as an "asshole" hero who saves people but destroys property and endangers civilians as a result of his drinking and a bruised amnesiac brain that can't remember his early life. As Hancock he must confront human beings today, not barren post apocalypse as in Legend. He rehabilitates his public profile, sobers up, and contends with his attraction to his "publicist" Raymond's (Jason Bateman) wife, Mary (Charlize Theron).
In other words, Hancock is not your garden variety super hero although he can fly and destroy with the best of them. He is conflicted about his weaknesses, his feelings toward Mary, and his forgotten past as a hero who may span thousands of human history years.
In addition, the allegorical implications about The USA as flawed heroic nation imposing its will on small countries such as Vietnam and Iraq seems to lie underneath this commentary on pop-cult heroism. Even if you don't buy that aesthetic, consider the Star Trek theme of the gods envying humans even with all their emotional messes.
Hancock weakens when it plays for laughs the heavy-duty existential attitudes of personal responsibility and at the same time looks for philosophical ballast. Star Trek did a better job of contrasting the lonely perfection of the gods' world with the robust, loving, but terminal world of humans. Hancock does a credible job showing how immortality without love is bound to lose to the glorious imperfection of mortality.
"Oh, He hath made things worthier than Himself,
And envieth that, so helped, such things do more
Than He who made them!" Tennyson's "Caliban Upon Setebos"