As far as mental scaring is concerned, having her assaulting the male athletes would be much worse. Cops are mostly use to that sort of thing, male or female. Not sure how it is in Japan, but in good ol' Murica, female cops have to deal with half and fully naked men. Anyway, I realize I'm overthinking it, so it's not really a big deal.
If I truly wanted to nitpick I would point out that women wouldn't be as inclined to wear short skirts and makeup in this alternate universe, men should be the ones dressing up. The point of dressing up is to draw attention to the parts you want people paying attention to. If guys in that universe aren't interesting in boobs and thighs, there's far less incentive for women to dress up exposing those areas, but in this alternate reality they are still dressing in a manner that would appeal to mean of this reality. Yes, I realize this is because of intended audience of the manga.
Well, they've implied that tendency to appreciate certain body parts of the opposite sex still exists. I mean, horny women in the real world get randy over a firm butt or chest, just like they've had the women of this comic's world lust after, and when Amamiya was playing badminton against Ichikawa, the guys were admiring her tits, just not nearly as overtly as boys in the real world would have.
Also, as for your arugment about Japan and security guards... the broadcast was officially in a foreign language, so I figure it's safe to assume the track was
not in Japan. But, still... you have a point about jobs. I still think this comic's world would be best served as having women as the more aggressive gender, as well as the one in charge, even if they can't apply the same kind of strength as a man. It would make more sense, in my opinion, alongside the men as traditionally nurses thing, since it was pointed out in a comment way back at the beginning that nurses are women in the real world mainly because the military barred them from being armed, but still needed a task for them in the wars, so they ended up taking care of the wounded... so, to me, it would make more sense to have the women as the warriors and leaders and the men as the caregivers, in this world, if we're going to double-down on male nurses being more common and probably traditional.
But, well, this author didn't really do enough deep thought on his world.
