That LTT had lost some of his reputation during the war. After all, it apparently wasn't going very well and the Shadow was near winning. It's said in "The Strike at SG":

'At that point, a stalemate developed, and for nearly a year neither side was able to effect any gain despite fierce fighting,
but when the stalemate broke, the Shadow began to advance again, slowly at first but with ever increasing speed. According to the writer of that fragmentary history, "It was as if every step forward by the Shadow scattered the spores of chaos before it, and feeding on what grew, the Shadow gained strength, so that its next stride was longer, and the next step would be longer still."
Huge areas had been devastated to varying degrees by this time as the war surged back and forth around the world, and it was obvious that while the Shadow was willing to starve or murder a great percentage of the population in the conquered territories, the forces of the Light could no longer sustain a protracted
war. They were losing, being pushed toward inevitable defeat with increasing speed, and if they were to win at all, it must be done quickly.'

This likely caused some discontentment and discussions among the Lightside, if LTT is really capable to beat the Shadow, and eventually allowed other politicians like Latra to gain much influence. Thus I don't think it's that strange that Latra could convince most strong women and probably many men as well, that LTT's plan is too risky:
"Apparently a speaker of considerable force and persuasion , she [Latra] gathered a large bloc around her, but what assured her victory was an agreement she reached with every female Aes Sedai of significant strength on the side of the Light. (In the manuscript, this agreement is called "the Fateful Concord," though it was doubtful that this was the name it was generally known.) Lews Therin's plan was too rash, too dangerous, and no woman who agreed to the Concord would take part in it. [...] Lews Therin argued again for his plan, acknowledging the risks but saying that was now the only chance, yet Posae maintained her opposition. Belief in the danger of misplacing the seals had spread, and many more female Aes Sedai had pledged to the "Fateful Concord," including a great number who were nowhere near strong enough to qualify for the raiding party circle . Tempers and passions rose, and an apparently unprecedented division along male-female lines began to develop among the Aes Sedai in general, if not within the Hall itself. Finally the Hall decided to continue with Latra Posae's plan, and her people began working to smuggle the access ter'angreal out of Shadow-controlled territory. [emphasis mine]

This quote suggests that the strength of the women did matter and maybe even that Latra might have been ta'veren. In the end, LTT simply didn't care about the participation of women and did it on his own with his cronies.