If the idea is to have a neutral party call her out on her bullshit, the problem is that her in-universe bullshit is very different from what's disliked about her outside of it. In universe her bullshit is being headstrong, rebellious and yet always eventually right. Out universe her bullshit dovetails with that only in the "always right" part, since the other issues are mainly with how people around her react to her.
If there'd been a character around her that served as a true sounding board for her all along perhaps this problem wouldn't exist. On deeper reflection, while I still think it's a bit unfair to give the Kirks of the show a pass and come down so hard on the Burnhams, it does occur to me that McCoy was Kirk's sounding board. Not that he ever actually changed Kirk's mind, but at least it projected to the viewing audience as Kirk having someone around questioning his wisdom.
But at this late date I'm not sure there's enough to grab onto, as I said, because calling her out for being rebellious is hardly what most viewers want to hear. They want her to either just go away at this point, or somehow workably in show not be lauded, not be right, and yet also somehow not be so invalidated as a character that we instead tail off into some "woe-is-me what did I do" mode, something I think we all know will bother the viewing audience just as much if they have to sit through it.