He always comes in throwing tantrums and eating other people’s food in the fridge. He habitually keeps his mask on even though EVERYONE knows his Identity. Batman: “Oh, I’m meeting with Mr. Wayne tomorrow to get the check for the Justice League Rent, Okay?” And he runs around screaming “I’m the Leader! Nothing Goes on without my say so!” while everyone else is zipping around him at supersonic and supraluminal speeds.
The Justice League doesn’t expect very much out of him. He got on the team by winning a raffle. He’s like a Make-A-Wish Foundation recipient. And because he is by far the weakest “member” of the team, they let him do whatever he wants.
But beyond being intelligent, Batman really acts as a check for the Justice League and a humanizing agent. See, Batman fully realizes that he is essentially a man walking among gods.
A lot of people have already written on Batman’s intelligence: He’s a very good detective, tactically brilliant, and very creative when it comes to technology. That’s all true, though I would argue the rest of the league could easily fill this void. Wonder Woman is every bit the tactician he is when she wants to be, and Martian Manhunter probably outclasses him in intelligence.
That terrifies him, and that fear both allows him to empathize with the people the League is protecting and gives him perspective on what the League is doing.
Even the Flash and Green Lantern, who were both raised as normal humans, are so powerful that they can and have messed with the fabric of reality. But Batman knows that if he’s ever caught unaware any of the core leaguers could squash him like a bug, most before he could even register the thought.
In my opinion, the majority of the League is so used to being the good guy and exclusively fighting epic battles, that they don’t consider that their actions may scare people or have negative repercussions on society as a whole.
But Batman specializes in street level crime, mobsters, and corruption. He doesn’t just get to fight a big bad and fly into the sunset most of the time. Instead he has to work within a community and attack problems at a structural level, even letting bad guys get away to get a shot at more important targets.
And time and time again, the insights Batman has gained by having to fight crime this way have prevented the Justice League from doing some incredibly stupid things.