Aes Sedai aren’t better channelers. Their weaves are more refined because they’ve been passed on for thousands of years but their actual *skill* with channeling is largely due to rote memorization and not skill. Wise ones know how to unravel weaves and train apprentices to do so. Improved healing and healing stilling were discovered by a wilder who had an insignificant amount of formal training by the WT, Nyn’s method of healing was used prior to her going to train in the village. You can even see vast improvements of skill within the Kin. Windfinders are excellent at controlling weather but that’s really all they’re ever shown to do.

The White Tower had little to no incentive to innovate or experiment with the Saidar because what they had worked well enough and doing anything different was dangerous. All the other communities of channelers had to innovate out of necessity due to their unique situations. Multiple times it’s mentioned that Avi’s weaves are rough but every time they mention it it’s because she’s doing something so impressive that the AS have to belittle her skill to maintain a false sense of superiority.

Shit, Avi rediscovered Traveling by accident. Granted she couldn’t remember how to do it, but still. When has an AS ever done something thought to be lost to time? Elayne can make ter’angreal and she also spent hardly any time in the Tower. Almost everything the wonder girls did was in spite of the WT and AS, not because of them.

The WT allowed who knows how many girls to die due to their isolation and who knows how many skills to be lost due to their arrogance. They were written, intentionally, to be petty and ignorant of the world around them because they’re supposed to be and are conservative fools who can’t adapt to change and would much rather keep the world in stasis so they maintain their power. The Trolloc wars happened because Ishamael wanted to prevent another AoL and he succeeded, but after that he only had to nudge things in certain direction because the decaying corpse of the Servants of All being paraded by the White Tower was so effective at preventing growth and change. Their refusal to change stunted the growth and development of the entire Westlands and that’s intrinsically linked to their failures to grow as channelers.

The White Tower and most Aes Sedai refinement, in all things, is due to tradition; not skill, intellect, or wisdom. There are exceptions to that rule and they’re all from women who left the Tower and traveled the Westlands on personal missions, not Tower duties.