Most of the ones mentioned either A) killed once in stories that may or may not be canon anymore and then were so psychologically torn apart by it they literally swore an unbreakable oath to never kill again (Superman), B) kicked out or were almost kicked out of the League because of it (Wonder Woman, Green Arrow), or C) were former villains that want to be heroes and thus stopped killing because killing is something villains do.
And yes, Superman has a stringent code against killing, why they hell would he fight against the Elite over it if he didn't?