Not because refusal to do so would "un-Aes Sedai" her (it doesn't seem to have done so with Siuan, or Leane or, um, a certain uppity Two Rivers Amyrlin... ) but because it would've put her more in the role of that vigilante. She would be going rogue, denying the authority of both Tower and Amyrlin. Aes Sedai swear the Three Oaths; an Aes Sedai who refuses to do so repudiates one of their core principles. She'd still be Aes Sedai, but an Aes Sedai who wants to make her own rules every bit as much as Elaida and every bit as much to the Towers detriment. You know what would make the world even MORE suspicious than they already are of Aes Sedai who deceive and prevaricate to maintain nominal adherence to the Three Oaths? Catching an Aes Sedai in a lie that "proves" the vaunted Three Oaths are just another lie.