At Wars of Ice and FireWars of Ice and Fire, Something Like A Lawyer fields a question about the series ending with each of the provinces of Westeros having a female leader. His answer is, basically, no:
I personally don’t think that there will be a united Westeros at the end, but rather a federation of kingdoms. I don’t think there will be a female head of each independent kingdom, but rather they will be a generation that isn’t considered ‘perfect’ by the past generation’s social structure. They will be women (Asha), they will be bastards (Edric Storm, legitimized as a trueborn Baratheon), they will have physical impairments (Willas), they will care for their smallfolk (Edmure).
Sansa is a special case in that I don’t think she’ll stay in the North (though she will undoubtedly return there). I believe, as tied as she is to other kingdoms, she will strive her hardest to ensure that peace, trade, and justice remain between the kingdoms. A sort of honored diplomat and guest to all the Seven Kingdoms.
And sorry to say this, but Arianne is doomed.
I don’t know any more than SLAL about what the status quo will be at the end, but I have my own ideas. I agree with the idea of a federation of independently governed provinces. I don’t think each province will have a female leader, but a pattern I’m picking up from the series is that the men who are on track to survive are the ones who are willing to work with, and learn from, powerful and capable women.
Granted, this involves some speculation on my part, but the ending I foresee will show a strong positive correlation between men who survive and women who guide, employ, and protect those men. For example, Tyrion will make as much headway as he does because he’s serving Daenerys. I seem to be in the minority in the fandom by thinking Jaime will survive the series, but I do think he’ll survive the series, and he’ll owe much of his success to learning from Brienne’s example. Sandor will be alive and thriving at the end because he shows up for Sansa. Bran will be alive because of Meera Reed. Jon Snow is a squishy area, but if he’s in good shape at the end, it’ll owe a lot to Melisandre, and to working with Sansa. Theon will survive because he’s willing to work with his sister.
Meanwhile, Ned Stark died because he underestimated Cersei. Littlefinger will end up dying because he tried to use Sansa as his pawn. Robb died because he didn’t listen to his mother. Robert Baratheon died…because he also underestimated Cersei’s capacity for violence. Renly Baratheon died because he had no business becoming king, BUT ALSO because he underestimated Melisandre’s powers.
As for who’s in charge of the provinces at the end…I have some ideas. I may be wrong about Edric Storm, but I just can’t see him being in a position of power at the end. Who would legitimize him as a trueborn Baratheon? It’s not in Tommen’s interest to recognize him as a son of Robert Baratheon, and Daenerys would have no interest in acknowledging the offspring of the Usurper, either.
I think Edmure will survive the series, and he’ll owe much of his survival to sitting out the war at Casterly Rock. He may return as Lord of Riverrun, but the Riverlands have always been such a hot mess, they need someone made of tougher stuff than Edmure to be their overlord.
Willas Tyrell may yet pull through, and I expect Asha Greyjoy to be in power in the Isles at the end, but I also think Sansa will mostly stay in the North once the new status quo is established. I agree that Arianne is doomed. All the Martells are doomed, the legitimate Baratheons are doomed, the Arryns are fucked sideways, Cersei and all her kids are doomed. I like to hope the Freys are doomed, but the best I can realistically expect is that the new Riverlands overlord builds some new bridges along the Green Fork so the Freys have to develop other sources of income. I think there’ll be some power vacuums after the war, and the final status quo will depend on how those vacuums are filled.