Part of the Tower's problem is that for 3000 years it been virtually unchallenged. Yet it has had enemies but they were political or military enemies not forces that could command the One Power against it. If you look at the history of Randland after the breaking the Tower only had two major problems. The first was the Trollock wars and the second was Hawkwing. For the rest of the time they have had to deal with no threat that could completly destroy them.

If you consider a lot of the European wars fought before Napoleon yes there were some good generals but a lot of them were not so good. They had their position due to their rank and wealth and so what if they lost a battle or even a war. The nation might lose some land but it would never be in danger of being wiped out and it could have a rematch a few years later.

It was only when total war came on the scene with the Napoleonic wars when one's country was at risk of being wiped out that the rulers had to promote the best generals because they were needed.

The Aes Sedai are like that, and now they have real rivals who can destroy them, the shadow is moving openly, the Seanchan have attacked them and the Black Tower is a real danger. Now they face a steep learning curve but if they survive they will come out stronger with good effective commanders and structures in place to actually fight a One Power war.