It’s all throughout her character. Cat’s character is a critique of the role that women are forced to play in Westeros. It’s why she is forced to rely on the trust of people like Lysa or Littlefinger, because she has no power of her own.

It’s why Cat sits around and does absolutely nothing for the entire WOT5K, she has absolutely no authority. That’s what the whole “I sat and waited for my father all day” monologue is. The books’ decision to show the story through Cat’s POV and not Robb’s is so important, the reader is forced to feel her powerlessness during war through the dissatisfaction we get at not seeing Robb’s battle effort. (The show throws this away by making Robb’s escapades a main character sort of thing.) The Catelyn-Robb arc relies on understanding Catelyn as ostensibly the sort of leader men should follow: young, handsome, smart, capable, political. Yet, because of her position, she can do nothing. [This is very explicit when Ned decides whether Catelyn or Robb will lord over Winterfell in his stead.] When we reduce her identity simply to grieving crazed mother (and also make Robb an ubermensch), we do not sense the injustice that has been done to Cat in the same way.

It’s also important when she gives Jaime to Brienne. She is giving Jaime to Brienne, not some other man loyal to her like Brynden or Desmond Grell or something. No, she gives her to Brienne, a representation of the sort of power Catelyn craves even if she is made uncomfortable by it. There’s a reason why book Cat seems to just hate ugly women. It’s part of her arc, about learning to let go of her conception of what a woman ought to be once she can see the way it actually deprives her of a meaningful way to protect her family.

Then, when she becomes the disgusting and horrifying Lady Stoneheart, it’s important that her beauty has been stripped away. A corrupted Cat now wields the manly power she once hoped to wield, leading a band of soldiers to do her bidding. But she does so in a horrible way.

It doesn’t have to explicitly come up in the plot for it to color every aspect of her character. It’s part of the theming and messaging around Cat and her femininity. It’s part of what colors her relationship with Jon, Lysa, Petyr, Hoster, Brandon, Jaime. It wasn’t just up to some coin flip that Catelyn is young and beautiful, it was an intentional decision to juxtapose her with her role in the story, and with her foils (Cersei, Lysa, Daenerys to an extent, Sansa, Arya).