2. They're Badass Warriors From Other Realms
At the beginning of Thor: The Dark World we see our hero fighting to defend the Nine Realms. The movie opens with a battle on Vanaheim, and shows Thor easily taking out opponents and ending the conflict. Like Thor, Hawkman is a badass warrior; he's just a lot more dangerous.
Hawkman is famous for his short fuse; and has been known to take out his anger on those he disagrees with, including other members of the Justice League (he doesn't much care for Green Arrow in particular). He's one of the few JLA members who isn't afraid to spill a little blood to do the right thing, or kill when necessary. Placing such a ruthless character in the middle of more morally-centered heroes like Batman and Superman could add a
lot to a Justice League film and add an interesting dynamic to their partnership. Hawkman has had several origin retellings over the years, one of which makes him a policeman from the planet Thanagar, who decides to stay on Earth and protect it. This of course is similar to Thor's story, and something DC could use to open up the more cosmic or supernatural side of the DC movie universe.