Which would make her something like the resident expert on the subject, no? What experience does Birgitte have to gainsay her?

You mean when they rushed into the Panarch's Palace with only two channelers against what could have been all 11 and one of the Forsaken hanging around? And won handily? Or the time they took every precaution and laid low in Tear, only to be captured? Or how they went with a full escort of Kinswomen and soldiers in Ebou Dar to the stash, lost most of the soldiers, some Kinswomen and only snared one Black sister, who was silenced shortly afterward? Do think Elayne isn't conscious of the fact that bringing others into her BA hunts tends to get them killed or else compromised to betray her?

And it was worth the risk. The death of Vandene was only a scheduling technicality and Sareitha was not much of a loss, to catch two Blacks, not to mention exposing and eliminating the traitor in their ranks. The biggest problem with Elayne herself being risked is her effect on Rand and the loss of her children. Since we know that THAT won't happen, no biggie. The only other problem you cite is the possible danger. What is YOUR solution to "a house stacked full of BA"? Leave them alone rather than risk the precious Aes Sedai? Can we infer general cowardice in addition to tactical blindness as reasons against women generals from your responses?

Translation: "I don't have as many valid arguments"

One fight at a time. Get Elayne back with the bajillion channelers in the Palace. As it turns out, getting her back was the key to winning the battle. In any event, what is she supposed to do? Hold off on doing anything on the off-chance she might get captured? Ask her sisters to risk their lives, while she cannot risk being captured? If getting rid of the Black sisters costs Elayne the throne, that's the way it would have to be. The Shadow out-ranks a political rival as a priority. No matter how inept Arymila's rule, it's better to keep the Shadow out.

Yes there were difficulties in whom to trust, but sheesh.