It only "suits them" when there is something more important to do.
And neither of them ran away. Tuon was kidnapped, after trying to stop Mat from leaving. She might have held onto her dignity rather than putting up a useless fuss, but she was operating, from the very first line of her first appearance in the books, under the knowledge of a prophecy about Mat, to whom she had to stay close. And she was right. Elayne left the White Tower to help Rand, because she heard about a Shadow plot, and wanted to help her friends. Way more important than White Tower bullshit. The "runaway" story when she came back was a ruse to fool the clueless. Sorry you got suckered into it. The second time she didn't run away either, she was tacitly asked to go on the mission by the Amyrlin Seat, who wanted to give herself plausible deniability.

Her second departure did not cause any such damage. And Siuan set it up so she & the Tower could not be blamed for the departure, meaning there would be no political damage.

And the success of the Black Ajah or the failures of her friends to stop them would be worse. Do you even see how devoid of logic your position is? You are criticizing Egwene's critics who cite her leaving the hunt for the Black Ajah to pursue her own interests, and you criticize Elayne for putting the Black Ajah ahead of her own interests. Stopping the Black Ajah is arguably the most important thing, Elayne put other things on hold for that, while Egwene abandoned that, to pursue other things. There is a certain logic to what you were originally whining about, but no underlying rationale for your own position.

And I am not even one of those who fault Egwene for going to the Wise Ones, but if Elayne had not left the Tower with them, Nynaeve would have had to go it alone, if Egwene was to pursue studies in T'A'R (even if her studies didn't contribute much, there was no way to anticipate that when she went).

Her obligation was to oppose the Shadow, not hang around jumping through pointless White Tower hoops. Siuan pointed out that Elayne's death would be a cheap price to keep Callandor out of the Shadow's hands. Furthermore, there was little to no guarantee of her managing to achieve any of your prescribed advancement hanging around the Tower like a clueless background character. As important as Elayne is, she wouldn't be safe in the Tower with the Black Ajah running loose. She is the one who reasoned out that the Black Ajah must have a substantial membership if they could pick such a wide array of dissimilar sisters for their mission to Tear, so there had to be a lot in there. As Liandrin pointed out, as an associate of Nynaeve & Egwene, she wouldn't be safe alone in the Tower, and Siuan was definitely not competent to protect her.