If Arya does kill Littlefinger, it may bring her closer to Sansa
Sansa appeared to regard her sister’s sword skills and kill list with trepidation, perhaps afraid for Arya’s soul, perhaps afraid for the trouble it might cause in the Winterfell she now safeguards.
But if Arya carries out the final blow to Littlefinger, Sansa is also absolved of something: his presence, which she resents but tolerates to keep good faith with the Vale. Once all is revealed, and a call for his execution is finally justified, Sansa can wash her hands of the man who ruined her life. This would almost certainly bond the sisters, who have always had a challenging relationship. Sansa, the prim and proper, and Arya, the tough and fierce, deserve to set aside what makes them different and bask in reunion of their family, and the revival of House Stark.
A tightened bond also feels the logical conclusion of their individual narratives. Sansa has grown into a strategist capable of governing her land and people; her role as Lady of Winterfell is starting to feel permanent, now that Jon is off with Daenerys. Likewise, Arya’s humanity is slowly coming back to her. Her time with the friendly Lannister boys, her encounter with Nymeria, and her return to Winterfell haven’t yet set her right, but she already seems softer, less burdened. Their coming together would be the convergence of opposing attitudes, a theme of the season, and the series as a whole. As Jon tells Dany in the caves, about the Children of the Forest and the First Men, “They fought together … We need to do the same if we’re going to survive.” As the White Walkers approach, a unified Sansa and Arya would be a hell of a team, with Arya’s combat skills put to good use, serving a greater purpose.
In the Season 7 trailer, Sansa quotes her father in a voiceover that hasn’t yet happened but seems a distillation of these many points: “When the snows fall and the white winds blow, the lone wolf dies but the pack survives.” With Littlefinger out of their hair, and House Stark in full command of their ancestral home, Sansa and Arya won’t merely survive – they’ll thrive.