Not saying that I either endorse nor refute it, but the theory is that Targarians are either blessed or cursed. Targarians will either be a great leader (Rhaegar) or a mad tyrant (Aerys, Vyseris). We know Cersei is one ruthless See You Next Tuesday, could Jamie be the blessed to balance it out?
When Arya walked into that room to confront Sansa with Bran at her side, I knew Littlefinger was a dead man