just because batman has tons of money doesn't make him in charge, does he have a plan of attack in battle? sure but hes not the leader. most of the other heroes don't trust him especially when he had contingency plans to take each one of them down. which led to him being fired from the league. nobody ever has an issue with Superman, hes powerful and brave, everyone looks up to him even Diana. and when he tells you something 99% you wont say "no" unless you are the goddamn batman. Besides Tony Stark funds the Avengers but he's not the leader, in Earth's Mightiest Heroes cartoon he was, but later was replaced by a more trustworthy Captain America who was also the leader in the movie and current comics.
Batman was only in the cartoon half the time. Even in Batman Beyond cartoon the future Superman offers Terry a spot on the Justice League Beyond, mentioning that he could be a full time member where as Bruce was only part time.
well i may not have read every issue of the comic, but the last volume of JLA before new 52 had Black Canary as chairwoman, Bruce Clark and Diana just had their secret trinity meeting room