Hmm... the first arc was the origin... the second is to make Hal leave so Johns can continue with the ending of his Green Lantern Saga and to hook up Superman and Wonder Woman... the third is to continue the story of Aquaman and the creation of JLA which is the set up for Trinity War... which itself is the fourth arc and preparation for Forever Evil, which is the fifth, which is also the setup for Luthor to join the League... which is the sixth arc, where Johns also introduce Jessica Cruz who was teased at the end of his Green Lantern... after that, it's straight to Darkseid War, which has been set up in the first, and act as the ending of the saga.
So yeah, Johns League is less about featuring the League members but more about his plot and conflict, including the plot and characters from his other books and stories (Arthur and Jessica)