First thing is the entrance, and the feel. Because an invincible hero stopping some robbers with guns is something we've seen again and again, and because he so seriously overpowers the robbers, it's hard for a bank robbery scene to have any tension. But, because Hancock's (and Ray's) ultimate goal here is to make him acceptable to respectable America, there is an incredible amount of tension in whether he will screw this up and do something clumsy or assholish.
Or as Ray says as Hancock is flying in "Please don't hit the building please don't hit the building".
And we see him skid to a halt on the concrete, which is an awkward contrast to his previous method of just slamming in and leaving a five foot crater of asphalt. ("Uh, that was there when I got here." "Yeah I know what my street looks like.") Hancock is definitely trying to improve from his previously destructive behavior, but it's still bumbling and clumsy. This is a pretty good depiction of the "in between" phase.
This is in line with Hancock's Tourette's-like repetition of "good job" to everyone he meets as he lands. He's trying very hard to follow Ray's advice, and his nervousness in this shows. It's adorable (and pretty confusing to the cops expecting the normal asshole.) The depiction is semi-critical of treating politeness like a cargo-cult, where you say the words but don't mean them (more on that tomorrow.)
Now, obviously, bank robberies aren't a major problem plaguing America, and this scene is more an archetype than it is a practical discussion. The particular archetype actually seems to be about a battlefield and the trauma of war (remember how mired in Iraq America was when this movie came out, a visual theme constantly addressed by Berg and other "pop" directors like Michael Bay.) Guns are constantly firing (by who? at who?), heavy artillery rockets are even being shot, and cars are flipped as barricades. We even get a direct reference to the Iraq war thrown in, as the cop Hancock is sent to rescue is announced as the widow of an Iraq War hero.
This gains particular salience because of the GIANT BALD EAGLE statue in the middle of the battlefield, and the way the ubiquitous eagle motif can be read as a connection with (or even obsession with) America and her armed forces.
Frankly, if this were any director other than Berg (such as Nolan or Snyder) this entire scene would be a dream sequence. That's basically the style it reads.
Berg also can't resist taking a playful swipe at "political correctness" when he rescues the injured cop under siege.
HANCOCK: Do I have permission to touch you body?
FEMALE COP: Yes!
HANCOCK: It’s not sexual. Not that you’re not an attractive woman. Actually you are a very attractive woman. And--
FEMALE: Get me the hell out of here!
When connected to the villain's therapy scene, you can pick up a distinct disdain for upper class language about oppression, versus the practical work to directly alleviate it.
Fortunately Hancock stops the bad guy and rescues the hostages, which immediately cuts to a celebratory public dinner and no mention of him returning to jail. The hero has passed through the ritual, and can now rejoin polite society.