Perrin caused Mesaana to be pinned in an arena where Egwene had a natural advantage, through her (dishonestly obtained) teaching by superior Dreamwalkers, and her innate talents in T'A'R, while Mesaana had none of that, and would have simply fled, rather than get caught up in such a one-sided confrontation, if Perrin had not brought the Dreamspike. And then Egwene would have been back to square one.
There is no evidence that Mesaana was less proficient than Egwene in TAR. Their battle seemed very evenly matched. And the dreamspike trapped everybody! Egwene could just as easily have had her ass handed to her.
A person weaving balefire dies just as well as anyone. No matter how much balefire you are weaving, you have the same anatomical functions, and are no more or less protected than a non-channeler.
Except that Taim had the AS hiding and cowering even before he got Sakarnen. Egwene was a rallying point and changed the whole tide of that battle. She didn't only take out Taim but hundreds of Sharan channelers. It says so directly in the books.