I’ve enjoyed how the story has played out so far and love the characterization of both the main MCs and the important side characters, but—like you—I do wish there were more moments where Chateau proved her bounty hunter skills. It makes sense that she’d be weak against Son due to the nature of his character + backstory, but she has swiftly lost every battle she’s been in so far. And while I understand that she may not be as experienced as other characters, she has yet to have enough successes to counterbalance the amount of times she’s been the stereotypical damsel in distress at this point within the story. She has all of the potential in the world to be such a beast on her own—based on the few skillful moments that we have seen her have—but instead we’re subjected to multiple scenarios where she loses and needs to be saved by Son and/or another character. That being said, based on what we have seen happen to her bounty hunter co-workers, it would seem that everyone in her organization truly is inept at their jobs. I know this is a shoujo manga, but sheesh—even I can't suspend my disbelief enough to accept the idea that Chateau and her co-workers were skillful enough to form a bounty hunter organization, only to somehow survive by the skin of their teeth time and time again.
Anyways, I love Chateau's personality and what we’ve learned about her so far, but I’m really hoping that the mangaka balances her out better as this series continues. Especially, because I'm quite invested in how the plot has played out so far!