(Spoilers Published) Lady Stoneheart is kinda useless and she's probably going to be killed by Brienne in like chapter three
I liked Catelyn a lot for the first three books and while I did find the Red Wedding heartbreaking, I did see it as narratively fulfilling for her and Robb as well as thematically resonant with GRRM's worldview.
But what is the point of bringing Cat back as Lady Stoneheart? Like how is bringing her back as a firewight going to move the plot forward in a manner meaningful enough to justify degrading the emotional payoff of the Red Wedding?
A lot of people like Lady Stoneheart because she kills Freys and those people are not wrong for doing so but it also wouldn't be very interesting to read about when there's so much else going on and isn't really relevant to any of the plots and is also something GRRM is likely ideologically opposed to and wouldn't try and indulge the reader's Id like that.
Thematically some read her character as GRRM deconstructing that same kneejerk hatred of the reader's for the Frey's after the Red Wedding and subverting that hatred by making the Frey killer (stand in for the reader's sentiments after the Red Wedding) an undead insane person imminently threatening two of the fan's most beloved characters due to their insane stochastic drive for vengeance.
And while I do like this, I think Arya is a much better character to explore this. Not that I'm saying Arya is going to come back to Westeros and start making Frey pie, but that her story seems to be thematically aligning to say that sometimes you need to grow up and move on and let revenge go, even if the people you want to take revenge on really deserve it.
Plus the Frey clan can certainly get their just desserts in a number of ways in future books without Lady Stoneheart - Daenerys is invading, Jon might be crowned king, and the Others need to cross the Trident to march south.
On a wider narrative scale - I think the firewights and Rhllor are relics of ACoK and ASoS and moving forward will be mostly irrelevant beyond the politics of Volantis/Free Cities and possibly Melisandre bringing Jon back. Westeros seems to be in the throes or entering the throes of Faith of the Seven fundamentalism following the strife of the War of the Five Kings - there is no world where GRRM writes the Rhllor movement taking off in contemporary Westeros with the current High Sparrow much less everything else going on.
As a side note how does she even have followers anymore? How is she paying/feeding them? The Riverlands have literally been raped by years of war/banditry and winter is coming - why do any of these people care about killing Freys?
In regards to the Stark kids - would them meeting Lady Stoneheart actually mean anything to any of them? They all think Cat's dead, would seeing her as an insane zombie who can barely talk seriously emotionally impact any of them? Maybe Arya could euthanize her as part of Arya's own journey after returning to Westeros but like what's the point? She's dead already - Arya wouldn't feel bad, especially after all this presumed training with the House of Black and White.
In regards to Jon's resurrection - Lady Stoneheart is not necessary for Jon's resurrection when Melisandre is literally already there to perform a Kiss of Life, if a Kiss of Life is indeed necessary for Jon's resurrection. Even if Lady Stoneheart was necessary, isn't that kinda dumb and makes no sense? Thoros kisses Beric, who kisses Cat, who kisses Jon? The Kiss of Life has nothing to do with faith or supernatural will and instead functions more like mononucleosis.
In regards to Robb's crown - redundant. Robb's will already exists. Who would even want his physical crown? Jon? Bran? Do either of those characters seems like they would want it beyond sentimental reasons? It's a plot hole she even has it.
In regards to Jaime and Brienne - Lady Stoneheart is not killing either of these characters in the beginning of The Winds of Winter. I'm sorry it's just not happening.
Both we the readers and Jaime and Brienne as characters know that they didn't do anything wrong after she sent them to King's Landing in ACoK - realistically they both acted honorably and to the best of their abilities. There's nothing Lady Stoneheart can tell them that will make them regretful about this. There's no internal conflict here.
I've seen some people here say she could send them to find Sansa and Arya but she doesn't really seem to be in much of a (re)negotiating mood after being resurrected, and Jaime and Brienne don't have any real information to give to her to justify Lady Stoneheart not wanting them hung.
Even if she does send Jaime and Brienne off to bring back Arya/Sansa - what does she do until then? There are no other viewpoint characters in the Riverlands and there are no viewpoint characters anywhere near the Riverlands. She just putters around and kills Freys #137 through #211?
But then what is the point of Lady Stoneheart? Jaime and Brienne find her, Brienne probably kills her because that would be more emotionally meaningful even if it's still not that emotionally meaningful, then what? She even got a whole epilogue.
I think that when George initially decided to bring Cat back he had a larger role for her but after gardening his way through Feast realized he had nothing to do with her and is using her as simply an impetus to bring Jaime and Brienne back together for Winds to develop their relationship together.