The women are not at fault, and Latra Posae's movement contributed as much as Lews Therin in saving the world. With her without LTT's plan, the world was doomed. With LTT's plan without her, the world was doomed. In opposition to one another, the world was saved...

Lews Therin's plan was brave to the point of insanity, and flawed. It called for touching Shai'tan/The True Power directly in order to seal him, and that is the cause of the Tainting. TGS revealed this. Lews Therin still resents the women for refusing to collaborate, but he is wrong. Jordan revealed in a Q&A years ago that if mixed gender circles had implemented Lews Therin's plan, both saidar and saidin would have been tainted, and the method by which saidin could be Cleansed worked only if one half of the Power wasn't tainted. That Lews Therin doesn't believe, but it's a fundamental truth, coming from Jordan himself. Had Lews Therin proceeded as originally planned, the world was doomed. Had he done nothing, the world was doomed. Had Latra Posae's plan been implemented instead (a giant temporary shield around the whole area), we can't be sure but it looks like it would have left Shai'tan build-up his strength under the shield and eventually break it and enter Creation.

Latra Posae thought Lews Therin's plan "too reckless". The Fateful Concord's refusal to participate is what made LTT's plan succesful. The women's refusal is as important as the men's initiative. The two are indissociable, it took the combination of the two sides to save the world, just like saidar and saidin must sometimes work against one another, not only together.

Furthermore, Latra Posae's plan indirectly provided the mean by which saidin could be cleansed, so its role in the Pattern was essential - without it, saidin would not have been cleansed before the LB. That's how the Pattern was woven: LTT's plan was halted by the women's refusal to participate. As a result, he was stalled long enough so the women could build the Choedan Kal (that one day would Cleanse saidin). Before the women could implement their own plan (that it seems logical was also flawed), the CK AK got lost and not found until after the WoS (Deirdre's group eventually recuperated them in the early Breaking and sent them with the Da'shain, and this is how TDR ended up with them, the other AK were either lost or damaged so they couldn't be used). Because the CK got lost, LTT had no choice to resurrect his own plan, and to go on without the powerful women he intended to use in mixed gender circles. He succeeded, and without the women participating in the Sealing (we don't know if women fought at SG, the Fateful Concord was an alliance of women powerful enough for the Sealing, we can't be sure all female AS opposed LTT), saidar got spared, and because saidar was spared and Shai'tan was temporarily sealed off, the world survived. The women were there to destroy the men and stop the Breaking.

There may be a "perfect plan" that would close the Bore for Ages without major damages, but it's up to Rand to find it. The previous Age didn't. It had two flawed plans that were complementary, though the protagonists at the time didn't suspect in the least the real relationship between their plans: that the second plan needed to be stopped, because beyond the fact it likely would not have worked, it would one day offer the only mean to correct the consequences of the flaw in the first plan.

Now that the purpose of the CK has been fulfilled, Rand was pulled to destroy the CK, realising how terribly dangerous such Power was.