The problem is the show runners and Sansa fans try very hard for everyone to believe that Sansa has become smart and a great player. But her actions prove otherwise. From the time she met Dany she openly confronted her. If she had truly learnt anything from littlefinger she would've been more compliant and agreeable. She told Tyrion that men in her family don't do well when they travel south but then she hinted at making Jon king, to get Dany out of the picture. But to be king Jon would have to go south, so what's your plan?? And then she had no problem with Bran going south. And no she didn't win the BotB either. Littlefinger helped her due to his ulterior motives. What could she do had the knights of the Vale not shown up? Her army was already battle-weary and depleted.