The mistress of T'A'R on her own ground? Sure, for Nynaeve, that is a fair fight, but hardly what anyone would call "her own weight class." Don't be deluded by their apparent equivalence of raw strength.

Moiraine only surprised Be'lal by accident, because Faile served as her PMD and sprung Be'lal's trap, both saving Moiraine from the snare, and deluding the Forsaken into believing she was out of action. Plainly the Netweaver was ready for her and her precautions and stealth were to no avail. As it was, she only was seperate from Rand (and thus out of Be'lal's sights long enough to get her shot) because Rand knew she was an impediment to what he had to do and shook her off. Had he allowed Moiraine to accompany him, Be'lal would have made sure of her before he ever allowed Rand to confront him.
In short, the only reason Moiraine succeeded to the extent she did against Be'lal was a function not of her plans or choices, but Rand's decisions, in opposition to her. The opportunity only came up because Rand threw out her script and was playing his own tune.

But the point is, she wouldn't have them to work with - they'd have HER to work with. Moiraine, 20 years into her career, was still nothing more than a glorified errand-boy. The other characters, less than three years away from Mommy and Daddy are figures of power.

That is merely a reason why she WOULD be listened to. Not a reason why she SHOULD.

For no good reason, other than a sham reputation for "saving" Rand from a dangerous scenario she herself created. Rand would have been long gone from Cairhien before Lanfear finished her conversation with Kadere (and you could even question whether or not she'd have been as angry, since his news that set her off was undoubtedly inspired by his observations of Aviendha and Rand when Moiraine led them past his wagon: perhaps without that confirmation he might have phrased his perception of their relationship less affirmatively and hedged his report with caveats to make Lanfear believe he was only passing along gossip, rather than reporting a certainty). Moiraine's enumeratoin of possible results is confined to the outcomes of her bringing him down to the docks. With Rand, Aviendha, Egwene and Moiraine herself all looking out for Lanfear in Caemlyn as well as Rahvin, the chances of her completely taking Rand by surprise and killing or carrying him off grow significantly less likely. However, in the free-for-all of a pitched battle, the chances of Moiraine claiming sole glory for saving Rand's life are dramatically LESS likely. What is far more plausible is that Moiraine saw her continuing to dwindle and diminish in comparison to Rand and losing all but cursory influence, even as he went on to break the world and make her sisters bend the knee and swear to him.

With so much to gain personally from the scenario that happened entirely and solely through her machinations, I will need a lot more than her fading memories of ter'angreal to believe that her plot was either purely altruistic or the only desirable outcome for Rand and his cause.

It never ceases to amaze me how for one character who constantly acts to protect her own influence and reputation, people are willing to take her words at face value and praise her apparent blind trust in a future-vision; while another character is constantly chided for her adherence to Min's far more reliable viewings, when that adherence is actually no more than lip-service to quell the well-meaning who would inhibit her efforts for the greater good.