One thing I would hasten to point out is that despite knowing of the reality of the Black Ajah (although they believe it to be small, probably 30-40 maximum) Moiraine and Siuan are primarily concerned with the Red Ajah and quite frankly the majority of the tower. A man who can channel is a grave threat to thousands; the Dragon Reborn is basically prophesied to be the second breaking (and worse than the first) I refer you to the reaction Moiraine and Siuan have to Verin when they discover that she knows.

TGH Chapter 7 Blood calls to Blood.

“Verin, Verin.” The Amyrlin shook her head wonderingly. “You accuse your sister—and me?—of. . . . I won’t even say it. And you are worried that you’ve spoken too familiarly to the Amyrlin Seat? You bore a hole in the boat and worry that it’s raining. Think what you are suggesting, Daughter.”

…

“Why are you telling us this, Verin?” she said aloud. “If you believe what you say, you should be telling it to the other sisters, to the Reds in particular.”<!