Explain me CrossGen

And while that may be true of the concept, GL, has far more often been played as a superhero, while Hawkman actually has been used as space cop way more often.
Anyway.

Yeah, "a lot of his comics" there = "the Green Lantern Corps mostly." Green Lantern's a superhero largely because he's in a superhero world -- the costume's a uniform, the secret identity's not very important, etc. Or maybe "he's only a superhero when he's on Earth."

A lot of CrossGen's launch stuff was much closer to that -- power as something granted/inherited, with responsibilities attached, not as a product of accident or personal design, with the conflicts closer to the GL scale than matters of vigilantism (some of this is because -- or why -- Ron Marz wrote at least one of the launch books).