I saw absolutely nothing wrong with this setting. First of all, how do we know Chifuyu gave her sword to Ichika? It was a similar sword, yes, but as far as we know, the mysterious core might dictate what manner of a weapon materializes, based on the person. And the core might give a shit about the suits being used (right now) only for nonsense show business instead of real warfare. The scientist behind them sounded like a difficult person to deal with anyway.

On the other hand, if the sister did give such a sword, what's wrong about it? She's an ace herself, is she not? If the dude can defeat any opponent while remaining with one unit of shielding on his own machine, he's the winner. It'll just be down to discipline and training. Chifuyu looked like the kind of person who wouldn't cut him slack.

The same goes for this duel. I'd say they let Ichika fight with an unform fitted machine on purpose. For those two this might have been an important match, but for the teachers and the academy it was a golden opportunity to see what a dude piloting a women only suit could really do, academically. You can always study him under controlled circumstances later but this was a once in a lifetime opportunity since Form Fitting likely only happens once.

Another entertaining episode. And I wasn't even going to watch this pile of cliches...