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.
Superman is the heavy hitter on Jla, their biggest gun, and so he is there to make sure that big time threats can be handled!