They grew and moved on. Moiraine, for all her contributions was still of the old guard, wedded to the status quo and more a part of the problem than the solution. In the pre-Dragon world, she was among the elite, but that was a time of age-old hierarchies and long-established status quo with a dearth of changes or developments. She demonstrated an inability to cope with the changing world and by tFoH had retreated to a limited role, only emerging to play a role when she was sure of her ground, but vastly out of her depth for the most part.

That is the key difference between Moiraine and the main characters - they progressed by making the most of changing conditions and turbulent circumstances, while those same factors undermined her authority and limited her ability to influence events.

Another area of her insuitability is hinted in her first chronological appearance, in New Spring, the novel. The shallow reader in the early books might question why the heroes are these farmboy losers and not the awesome and cool Moiraine and Lan, but we see their weaknesses in the prequel. Moirine flees the Tower rather than stomach what she (possibly erroneously) believes to be necessary methods to rule Cairhien, when the early days of the characters all assuming roles of authority includes their learning to deal with these same distasteful aspects of responsibility. While Moiraine has grown up a bit by the time of the main sequence books, the flaw she notes in Siuan in tGH is consistant in her characterization throughout, if in different ways and to a lesser degree.

Rand's character flaw in the last book is the exact inverse of the sisters' - he is all too willing to do whatever it takes (however much Moiraine asserted her willingness to do just that, she had limits; conversely, however much Rand declared his revulsion, he never shied from a truly necessary action), and must find his moral center lest he take that to too great an extreme. With Rand the question is not if he can win, but if he can win properly. With the Aes Sedai (of which Moiraine never stopped being one in spirit or deed), the question is always, can they man up in time to do what must be done, whether aid the significant parties or put aside their trivial preoccupations to turn their eyes to the critical issues.