The movie shows that each member of the JLA has a definite purpose within the team, as WW is the natgural leader and best fighter, Bats can improvise and has gadgets, AM can command the oceans and is physically on par with Diana, and Flash has speed, and is like their version of Spiderman, youngest one cracking lines and in hero worship mode! Cyborg has new god tech, and is privtol in movie.
Superman is shown as being their most powerful member, as it should always be...
If Superman is so powerful he can solve any problem the League faces by himself in moments you don't need the rest of the league. At best they do limited damage control while Superman does the heavy lifting. That is contrary to the Avengers where everyone is essential to the team. From the sounds of it, the only leaguer that may matter is Cyborg because of his superior ability to use technology.
The only solution then is to break out the green k to remove Superman from the story until the League can get him back so he can save the day in the end.