The reason for Batman's absence in the series is...
He ended in a dimension that happened to be the Revolution. It took him quite some time to find the means to escape and get back into his own dimension. Evidently, his call to Alfred at the end of the show demonstrates his success in returning. If the series lasted past 2005, Jason Todd would show up as the Red Hood.
He was only mentioned on the show. It would have been revealed that he was indeed killed by the Joker and is Back from the Dead.