It's less about Hawkman being a reflection of Batman, and more Hawkman having his hands dipped in every little corner of the DCU because of the reincarnation cycle angle.>>107791325
The whole "Tribe" thing is an old DCU concept that pretty much came from Vandal Savage and Immortal Man's backstories. Savage coming from the Bear Tribe and Immortal Man from the Wolf Tribe. Grant Morrison then introduced the idea of the Bat Tribe in works. Snyder is just adding Hawkman to the stew with the Bird Tribe thing.
And really, Scott Snyder for some reason just really fell in love with Hawkman for some reason and wanted to make him the most important character in the DCU. He even wanted him to be a big player in his Justice League run, but editorial again stopped him. I kinda get it,since otherwise he'd be messing with Venditti autonomy.