Being in leadership implies no such thing, and especially not where the Shadow is concerned. No one serving the Shadow is in it for the cause or for the Dark One, they are all in it for themselves. Leaders are promoted because they are better at climbing the ladder, regardless of what sort of results they get. A member of the Supreme Council of the Black Ajah with the leadership approach you describe would best be diagnosed as suicidal! A laissez-faire management approach to leading DARKFRIENDS is the best way to be assassinated, ESPECIALLY for a hyper-competant subordinate! The Black sisters who are very good at getting things done are the ones who are the prime targets of their superiors' attention! Now granted, if anyone could divert her bosses' suspicions it would be Verin, but that would be through hiding her ability to get things done. And bear in mind that she was a reluctant Black at best. She might have unflinchingly committed atrocities to maintain her standing and cover, but I doubt she showed any more initiative in her duties as a Black than she absoltely had to.

A final point regarding information - either the Supreme Council members all DO know everyone, and that is one way Verin could have got the names, in which case every other member of the Supreme Council would have access to those same names, and would be keeping a gimlet eye on one another, as the most dangerous potential rivals, making the Supreme Council a very unattractive position for Verin & her mission; or they do NOT generally have that information, in which case there is absolutely no reason for Verin to aspire to that job. And for Darkfriends, there always is someone willing to step into an authority slot, so it is unlikely she would been forced up.