Allow me to both clarify and modify my statements; I wrote that at about 2:00 am last night when I was quite tired and slightly upset from zero quality bestgirl.
I misspoke; Yukinoshita is essential for the series. Or, at least, she was. It was thanks to her that 8man even joined their club, thanks to her that Yui became a part, and thanks to her that we got so much character development in the first season. The dialogue exchanges between Yukinoshita and 8man were some of the most enjoyable parts of the first season; their contrasting personalities and different views of the world despite both existing as outcasts were fundamental for both explaining and developing 8man's personality. In addition, the conflicts between their respective characters and viewpoints were the reason many of the tasks they handled ended up the way they did.
Cue season two. The first mini-arc felt as much a continuation of the first season's style as any, and Yukinoshita played her part. But her character is, and was, becoming dry. I understand she's confused; she doesn't understand the fundamentals of 8man's character and every action he takes seemingly betrays her expectations. Yet at the same time she treasures her bond with him (or at least with the club as a whole) and so she's torn between embracing the things she values and rejecting the things that continually make her uncomfortable.
The problem is that we, as the viewers, don't have access to her thoughts and inner monologues. We get plenty of 8man, yes, and it's largely thanks to that limited omniscience that the series has succeeded so much thus far. But from the viewer's (and 8man's) perspective, all Yukinoshita does is complain. She sits there in her shell and acts distant and bitter. When people reach out to her, she stabs them in return, and when people take actions she doesn't agree with she rejects them altogether. Then she holds grudges and refuses to let bygones be bygones without melodrama.
She played a huge role in the first season, but now it seems she's just there to provoke conflict and draw out drama. Maybe this arc is just an outlier, but there's no counting on it. In any case, I've never been especially fond of her type of character and her recent actions on top of that just hurt her (in my eyes) even more.
I wish we, as the viewers, got access to some of her own internal monologues, since I feel that could make her a much more sympathetic character than she is right now.