If I remember correctly, the DC arm of Warner actually has to pay the Cartoon Network to air their shows (similar to how Anime studios have to pay Cartoon Network). It's like a company buying a commercial except that it's a 30 minute block. Cartoon Network is also making money off the additional commercials during the show, but at some point I guess they consider it not with the company's fee.
It would be kind of like how businesses did away with pin ball machines in favor of arcade games - even if the arcade game only made the same amount of money, it took up less space which allowed for another product to be placed and make more revenue. A Cartoon Network original in place of a DC show would make more money for Cartoon Network.
As for why two arms of Warner would not cooperate with each other? Ted Turner designed it that way on purpose. Ted wanted the divisions competing with each other; he thought it would make them better.