I think we're pretty much on the same page, right down to not liking the Nolan films.
I think there's an audience for more complex female characters, and female characters who aren't noted
only for their sexuality. The Last of Us was a game starring an LGBT 14 year old girl and it was hugely successful! Content creators are simply -- frequently -- behind the curve. Or just suck.
Incidentally, the art design in the Arkham games particularly as it relates to the characters is really horrible IMO.
I can't speak with too much nuance on the comic side of things because I haven't read a lot of western style superhero comics, but I did watch Batman TAS extensively growing up. Most people I knew did. It was a memorable show.