There's Only Room For One In The Captain's Chair
The arrival and introduction of the Amyrlin Seat finally puts a face to a name, so to speak. Her authority is vast - spanning the entirety of the known lands. The White Tower has Aes Sedai from (nearly) all lands and peoples, giving The Amyrlin Seat a web of Sisters with inroads to influence and shape world events. Chosen by and raised from her peers, the Amyrlin Seat is of all ajahs and of none.
Suddenly she threw her arms around Moiraine, a warm hug between old friends; Moiraine hugged back as warmly.
"You are the only one Moiraine, with whom I can remember who I was. Even Leane always acts as if I had become the stole and the staff, even when we are alone, as if we'd never giggled together as novices."
Moiraine and Siuan, The Great Hunt, p. 50
Leadership is hard. And it's equally as hard on the leader. The pressures of the position are unrelenting. And it's lonely - the responsibility rests upon the leader alone. The rest of the team actually drives the success (or failure) and produces the results; but the ownership rests upon the leader. It's important for leaders to have trusted people outside the immediate hierarchy or organization to act as sounding boards. Part of it is to benefit from similar experiences and different perspectives. Perhaps the more critical advantage is that it provides an honest assessment. Everyone in an organization has aims, goals, and desires. Often they parallel the overall organizational goals; sometimes there are divergences. The divergences may be slight, and a trusted sounding board can help wrestle ideas and work the situations back to the leader's advantage.