I'd say Batman. I mean, all off his specialties are covered by all of the other members:
Stealth: A guy who can fly, turn invisible, sheild himself from all telepathy, and walk through solid objects trumps a ninja any day.
Tactics: Wonder Woman was trained in several forms of armed and unarmed combat and military strategy from a very young age and has proven herself an equal to a living personification of war in both fighting prowess and tactical thinking. Aquaman is an acomplished military leader and a highl savy politician, well versed in many methods of psyhological manipulation. I'm not saying they're better than Bruce, but they certainly cover that territory.
Science: Bruce is smart, and he knows alot about mechanics, electronics, forensics, and metalurgy. But John Irons is a brilliant inventor and engineer and one of the top weapons designers for the military, and Ray Palmer is a world renound physicist, chemist, and inventor who's often called in as a consultant during disasters.
Funding: Aquaman can easily fund anything the League needs, having access to vast treasure troves of sunken antiques that he has little use for. Plus, as ambassadors to the U.N. who often assist U.N. peacekeeping forces abroad, Diana and Orin can easly influence the U.N. to bankroll the League as they (the U.N.) have in the past.
Detective work: People forget that Superman is a highly inteligent and succesful investigative reporter. He's obviously not as good as Batman, but the league rarely has mysteries that require world class detective work.
Really, he's only there because he's popular. If he was brought in every now and then as a consultant for organized crime related cases and the occassional tricky mystery, that's make more sense. But it wouldn't be cost effective.