Gigi might've been curious but with White wanting to push her acting career she might've kept it to herself. I mean, with how White freaked out over how Nite would've looked like, ruining Gigi and Tep's image as a duo (before figuring out a way around it), I'd be hesitant too. That or White told Gigi that battling could be determent to her acting career and image.
And as for N, again he's opinionated as all hell so to him, he makes sense. Well, speaking about himself only.
As for White, while I don't mind her character overall (her girly personality is nice), I do agree her Trainer skills could've been showcased better. I hope that she reappears in BW2 (particularly when PokeStar Studios) to show that she hasn't been slacking in being a Trainer. A good battle against Neo Team Plasma should show that she can hold her own. Hell, I hope Black reappears unlike in the games where you're PC can't be found.