I agree. The whole thing about genders is a huge part of her story.
Does Genderswaped Yuu kinda look like Labrys to anyone else?
You know, Naoto would still be a detective, and given that he male he wouldn't need to Crossdress as a Girl in a male-dominated job. The Only that'd work for him is his being a Young Boy, but want to be taken as a Man.