I disagree because everyone is focused on Littlefinger driving the wedge all by himself. But Littlefinger uses wedges that are already there. This one is simply not common knowledge. Listen to how the North reacted to the summons. “Targaryens cannot be trusted.” So what happens when Jon’s parentage and real name breaks? Does the North want to be ruled by a dragon, even one that is half wolf? He did let the wildlings past the wall, and they didn’t hold the white walkers back. (Predicting that last bit.) There’s the wedge, the old great house fighting, Montagues and Capulets. All Littlefinger is doing is making sure the idea of taking power has occurred to Sansa before the moment presents itself.