Why doesn't another character's assessment matter, though? And Verin's statement that she riled up her (Black) associates is a statement of fact, backed by the fact that in one of the first instances of Egwene trying to bridge the gaps in the Tower, a Black was present and had to do what Egwene suggested.
You're right that anyone could see sense and do what Egwene did. Heck, Saerin, or Tarna would have come up with these ideas with their eyes closed.
As I said elsewhere, they had two disadvantages. One, they couldn't go from Ajah to Ajah. Two, they were themselves caught up in the pettiness and infighting, and these had come too far along before they realized that had happened to the Tower.
So, Egwene provided fresh perspective, and yes, it was Elaida's blunder which let her do that. But in her position, not every person is going to continue to speak to Aes Sedai and give counsel when doing so results in beatings and penance, rather than reasonable acceptance, more often than not. A Cadsuane or Nynaeve would have provided the same perspcetive, but would have completely lacked the patience to deal with these idiot women. Egwene remained invisible to Elaida, but was able to encourage cooperation by speaking to members of each Ajah in a language they could understand, making each see that their Ajah's purpose was well suited to heal the Tower.
Frankly, the only other character I can see having success in a similar scale is Elayne.

You must realize Cannoli, that if your reaction to Egwene improving in this book is to post a pages long rant against her, then your perspective is wonky, and no one can be blamed for thinking you were blindly criticizing Egwene.
As for taking action anyone could take... didn't you praise Elayne for increasing the size of the Queen's Guard and using Gateways to supply Caemlyn? Both are total no-brainers, and any Queen would have taken such actions. It is hardly a stroke of genius to expand your army when you are the leader of the third and weakest faction fighting for a throne! I, however, can see that being absorbed in tradition and a myopic worldview prevented Dyelin from approving such action. Much as so many women in the Tower failed to see how entirely normal Egwene's suggested course of action to heal the Tower was. And so, I too praise Elayne for making these decisions that expedited her ascension to the Lion Throne.
Also, I think you praised Elayne for not running back to the palace and instead using her rescue force to encircle Arymilla? That is a tactical decision that requires no great thought. Anyone whose primary priority was success in the quest for the throne would have suggested that. Birgette did not because she saw protecting Elayne as the primary priority.
Egwene too has done many things that any Aes Sedai could have. But they did not, caught up in tradition or pride or the nets of the Shadow. And she had some of these issues too, but overcame them and rose to the challenge, undoing Mesaana's work and saving the Tower from complete disaster in the hands of the Seanchan.

It seems to me more like you think Egwene's cause is less worthy than the others, thus her achievements are inherently cheaper, in your eyes.

While it is a whole other debate whether the Aes Sedai are worth the effort of saving, the point remains that Egwene has done a good job of ending strife within this organization. We shall see how she wields its power now.