well, I recall that all especially lucky males were targeted during the Vileness - not only channelers : The Vileness | A Wheel of Time Wiki | Fandom : Immediately [Jarna] started a great hunt, an even more intensive search than usual for men who could channel - for every male of any age who showed any sign that they might be able to channel or to be a ta'veren. Even a rumour, a hint was enough. And since being lucky or having a sudden rise to prominence were among the signs to look for, it was a very bad time for men with a bit of fortune. For that reason hundreds of men were killed secretly by "accidents" engendered by Black sisters. When that was not possible, they were accused of being channelers and killed with the excuse that they were "trying to escape" or the like.

You already had the Red Ajah hunting male channelers for millennia in Randland, while Seanchan had a systematic culling, Aiel went to the Blight to die, and in Shara you had the male Ayyad as breeding stock. Another point not discussed for Randland is 20 years before with the Vileness : Red Ajah overhunted potential male channelers, manipulated by the Black Ajah. So I would say a lot of potential male channelers went into hiding then - and they had no reason to go back afterwards, until Rand's proclamation.

Reading the thread above, I guess one part is not very much discussed : yes Egwene was an ambitious young woman when leaving the Two Rivers, and then encountered Moiraine which was an ideal Aes Sedai - which could have influenced her. At this time, she has no strong beliefs about the White Tower, she still is somewhat overwhelmed by the White Tower - maybe thinking all Aes Sedai are like Moiraine - and that she can help Rand from within. Then she is tricked by Liandrin, and becomes a damane under the Seanchan at Falme - unlike Elayne and Nynaeve. She is tortured psychologically, and we know that even experienced Aes Sedai are broken under this kind of treatment. I think she was a damane for weeks or even months. Now imagine the impact of such torture on a 18 years old. Her survival instincts say that she doesn't want to be collared anymore. What is the best, no, the only way to do so ? Only by having a strong White Tower to counter the Seanchan. So yes, Egwene is seen as very driven about the White Tower, unlike the other protagonists. But she was also traumatized in ways that no other protagonists encounter - until Rand is forced in a box.