In going to plat devils advocate here, I say this because I HATE Tywin almost as much as anyone because of his use of the mountain-his treatment of tysha-and most of all his use of e bloody murmmers, and say IF head lived long enough,which really is predictable go n his health and situation at the time, his rule was almost a strategic masterpiece. IF he was alive there would have been NO faith militant. He would have placated them in some way WITHOUT giving them the right to arm themselves. Cersei would have never been tried if the faith didn't have didnt have a armed militia in front of the sept of baelor. The Tyrell's still would have powe but would never be able to over reach themselves with tywin still alive because they would know Tywin is not a man to trifle with, ask house Reyne-Tabeck-stark, and would ask for power but never as high as hand of the king like Mace gets. Although Cersei is obv incompetent Jamie's leadership skills are not just because of his transformation after his time with Brienne, she didnt teach him anything about diplomacy or sieges. I would say his success in his two sieges in AFFC was due to prior tutelage, from his father maybe? You also speak of how much more loyal Starks bannermen are but what evidence do you see of disloyalty among the Westerlands bannermen? I've seen none so far and would say even after his death the bannermen of the Westerlands and casterly rock are Mong the most loyal in the kingdom at this point. Tywin was also very open handed with his bAnnermen, or so Ser Kevan lannister says, which is a great way to install loyalty. The iron bank also would have NEVER backed stannis as long as Tywin was alive. WORST case scenario he pays them with Lannister gold, which Kevan thought might be inevitable, and kept the as unitnterested in westrosi affairs as they had been in the first four books. So with my points above I think I pretty well dispute most of your issues with Tywins issues as a leader