This theory is about the disadvatnages for Halima from Egwene's kidnapping and the advantages for Halima from Bode's kidnapping (as Halima expected, before Egwene's intervention). I'm assuming here, it was Halima, who was responsible for managing the kidnapping: I haven't enough evidences about prefering this variant before the alternative traitors, but it is one of the best alternatives, and it would be very ironical for Halima to ruin her own plans by her own acts, and because "WoT" is a novel with lot of ironical peripeties, it's a little more likely variant. But even if it's not Halima, who telled to the Tower the chain transforming plan, it's consequences for Halima's plans are the same.

Most likely Halima knowed about Egwene's plan, she knowed that it will be Bode to perform the mission, and she didn't know Egwene's taking part. And she (or whoever else made the deal with the TV sisters)expected Bode would been captured. Why wishing Bode been captured? Bode is a novice (a novice!) sent in a dangerous mission. And novices are regarded by AS as children. Including the aspect, that accidents with novices are regarded like accidents with children. If an AS as Kairen Stang would be captured by the mission, it would be bad for who ordered the mission, and the rebel Hall will be very angry. But the difference between AS captured and novice captured is like the difference between a soldier MIA and a child victim. A novice captured is a great scandal, a perfect bomb for Halima to throw in the rebel Hall. Amd whatever Halima's plans are, they do include maintaining as nervous as possible atmosphere among the rebels. And concerning the advantages for the Towes AS from the "bargain" some points: 1. it's not necessary for them to know it would be novice, they will expect a full AS to perform such a mission; 2. the bargain coul also include Leane's kidnapping; 3. tha lack of novices in the Tower makes a girl with Bode's abilities something precious; 4. the scandal of sending a novice in such a mission is very well for Elaida's propaganda.

But in the last moment and without any warning, Egwene takes part and goes to transform the chain instead of Bode, and the situation is changed radically in all the aspects.

1. Amerlyn captured i much worse fo the rebels then a novice captured, but it's a completely different kind of scandal. Halima's actions maintained a status quo of ineffectivity, but Amerlyn's kidnapping will cause some radical solutions, it may ruin the rebellion or it may consolidate the rebels or force them to a decisive action, but it will radicaly change the situation in a way unexpected by Halima, and very possibly in a way unfavourable for her. In any case her plans concerning the rebels will no much mach the situation and will require too radical changes, with enough time to react. Even if it would create chaos, most likely it wouldn't be the sort of chaos Halima wanted.

2. Halima's massage sessions require Egwene presence, and Egwene is no more present. Whatever Halima intended with her massages, it was one of her primordial objectives to be near Egwene, and now she's not. By Egwene being kidnapped an important part of Halima's plans is ruined. Ironically by being captured Egwene escapes a great great danger, against wich she showed no abilities to defend herself. At least now her deraming skills will be no more threatened.

3. Actually it's not the best time for the Tower Black Ajah to face such an important event as the enemy's Amerlyn captured. Actually the situation in the Tower BA is very delicate now. The resident Forsaken is in very difficult situation and there are to be expected more troubles then help from here. Shaidar Haran is now in charge, but SH cannot be long time far from Shayol Ghul, and he's also busy with another things, so now the Tower is almost without a Forsaken command. The situation with the Black Ajah Head is even worse. Alviarin is still Head (i.e. regarded as unchangable without a Forsaken order) but she's in very difficult situation. She's very angry with Elaida escaping her control, and Egwene's kidnapping will strenghten Elaida's position much more, and enhance her arrogance too. This could move Alviarin to do something desperate. And in the time of her absence something could happen in the BA, threatening her leadership position. Because Mesaana was too calm about the lost control over Elaida, there could be another figure from the BA becoming more important. Katherine Alruddin came to the Tower in the same time as the new Keeper, she is very strong in OP and maybe the next Head of the Reds (Reds are leaded by the strongest among them, as BWB states), and there is maybe a special behaviour of the Shadow to her (her rescuing from the Aiel, when another BA remained prisoners. All that could move Katherin to claim the leadership in the BA. A struggle in BA could make it very difficult to use Egwene's kidnapping coordinated, effective and consistent enough. They will try to use it of course, but there may be too many incompatible plans only in the BA about, and nervous plans too. And because they are unprepared for Egwene coming in their hands, they will be put in the position to improvize, and it's not the best time for them to improvize. It's quite possibly for them to make mistakes attempting to react to Egwene's kidnapping in a too nervous way. And not to forget the Seanchan strike coming, what makes the situation even more complicated.