Frankly your just coming off as bigoted, you want her to fit a set mold of cross dressing and are annoyed she doesn't fit it.
I want the
character to make sense. You're making a bunch of assumptions on things we don't know and the fact that she's a woman. I'm criticizing the information we got this chapter about how she sees herself, and its weird and almost contradictory.
We're presented a cliche scene of a girl inheriting the special weapon of her family, much like Kate, but unlike Kate who was forced to cross dress to hide herself, Akira choose to cross dress because she thinks people look down on her because of her gender.
The story does nothing to present to us why she has this mindset. Her parents support her, and all of her training doesn't look to be toned down at all. In fact it looks like it constantly ramped up as she got older. So its weird that she thinks this way in the first place with not evidence of it.
The girl were presented with however is someone who does think these things of herself. She doesn't want to dress as a man but actively resents being a woman. Even before cross dressing she was bothered by her own body, sexually repressed or not. Her undressing in front of the other students doesn't feel like a forced act with that question mark hanging at the side. It makes her seem like someone who doesn't care about her gender at the least, but we're shown someone who cares a lot. She promised to return home but we can safely assume that her parents didn't, and wouldn't mind. When her Ego is set up that high and the story throws its cliche in the garbage that hard, its at least a little weird that she's wearing laced panties.
The real reason she's wearing those is that we're reading softcore porn. It makes sense for Kate to do it because she has actually been repressed. Its not about cross dressing correctly its about it not making sense for Akira's character.