In the general population, people marry young (16-18 years old) which is plenty young enough for Men to have not begun touching the source yet, and for some women. The sparkers and learners out in the general population are still adding to the next generations. Even then, some will survive the channeling sickness and keep channeling (perhaps with a block), and will continue adding to the genetic pool.

Aes Sedai do not reproduce often, and they continually take women from the same regions. Caemlyn, Cairhien, Tear, the Borderlands, the region around Tar Valon. They are actively removing the women who could breed up new channelers, heightening the culling effect. They also spend significantly more time in these regions, and so are more likely to notice the signs of channeling in a man. The people there are more likely to notice those signs as well. Those two things would make them more efficient at removing male channelers from their population, again heightening the culling effect.

In the more distant regions where Aes Sedai rarely visit, the culling effect should be much diluted.