Short answer to OP: When the world is falling apart, going through cataclysms and survival is extremely difficult - knowledge and organization is lost.

Also, just pointing out that the Hall of Servants fell during the War of Shadow, before the Breaking even started. As far as we have been shown, after this happened, the Aes Sedai were fractured and were no longer united as a complete entity before Lews Therin lead his strike. A lot of technical skills and knowledge had been lost even before The Breaking (we know this because ter'angreal and angreal creation had regressed sharply after the global infrastructure was destroyed). We actually saw some of this chaos when Rand went to Rhuidean. To give an example, almost all of the knowledge we have of how it played out is restricted to a fraction of one continent that had the Bore on it because the rest of the world fell to chaos during the War. We're talking about a civilization that fell from the use of flying cars, laser pistols and blasters to medieval weaponry. That's a catastrophic loss of technical capability.

Further, strength is not distributed evenly and there was no guarantee that it would even be identified in such a chaotic environment. It is a possibility that many channelers with great potential died during the upheavals before they sparked or could be found & taught. You could have an immensely strong AoL Aes Sedai completely cut off from other channelers protecting a community of refugees and all of their knowledge would have been lost because there was no channeler in that group to pass it on to. Vice versa, you could have a weak Aes Sedai that came across a survivor with greater potential, but the Aes Sedai was not strong enough to use some weaves without a Circle (commonly relied upon in the AoL) so despite having knowledge all they could pass on was basic skills. The system broke down.