Who can Anak even fight that's a challenge now? I guess she and Androssi can tag team vs the evil princesses...
I remember a SIU blog translation from three years ago where Anak told Androssi she was specifically climbing with Leeso & A.A. because she wanted to get to "The Floor of Death" where Enryu killed the Administrator. The Floor of Death is outside of Jahad's control, so that's probably the only place where princesses are free to do whatever they like.
I think we are carefully being setup for a massive plot overhaul, and chapter 293 kinda support my suspicion. Kaiser losing her name would make her subject to two contradicting laws, cancelling each other. She would have to follow Baam's wish, and she would no longer be bound to repay her family's debt. That's why Jyu Viole Grace is so precious to Kaiser: she needs to be under the command of someone whose objective is to end the Jahad regime. She wants to lose to FUG, not to anyone else.
The thing is, Yuri Ha knows about it. She probably sees an opportunity to present Kaiser to Wolhaiksong, rather than FUG, by way of Baam, and also as petty revenge against the Lo Po Bia family since her fight with Ren.
And that's only the beginning. There's a hell of a lot at stake in the Floor of Death, all sorts of conspiracies unfolding. What about the Prince of Jahard (Wangnan?), what about FUG, Cassano, what about that family head who brought the Thorn to FUG and oversaw the Workshop Battle?
Anyway I predict we won't see much Anak action until the Floor of Death, where she might get the Green April back from Yuri, and be reunited with Princess Garam.