Proposed Games: All of them
The Batman, set in a different continuity from Batman: the Animated Series, was admittedly very strange. While it ended up being the bad kind of strange, the show's first two seasons were very much so the good kind of strange, partly because of the original character Detective Ellen Yin. Ambitious, brave, clever, and armed with an unyielding sense of justice, Detective Yin started out working with the police department against the vigilante Batman, but the two soon form a partnership based on mutual respect.
In Origins, Yin would just be an officer, indoctrinated with the police department's policy against vigilantes. By the time Asylum rolls around, Yin would already be a detective, bent on containing the situation in Arkham. Throughout the series, just as it played out in the Batman, Detective Yin and Batman would slowly find common ground, becoming close allies. With Gordon as mayor in Knight's epilogue, Yin naturally would be made commissioner and all would be as it should and we could all finally get over the fact that Yin was written out of the Batman without explanation in Season 3.
What other Batman characters do you wish had cropped up in the Arkhamverse? Weigh in by commenting below!