The test is not in and of itself stupid. Aes Sedai live very long lives, and I get the impression that almost all of them have had to use the power in battle outside the Tower at one point or another. Look at all the instances in the books where the so-called "peaceful" Ajahs like the Brown, Grey, White, and Yellow have had to fight. Where would the world be if Verin had not been an expert at channeling battle? She successfully fought Trollocs at Emond's Field and dueled Graendal to a stand still: "She knew when she was fighting for her life...". At Dumai's Well, Aes Sedai of all colors had to fight against an army of Aiel attackers. Yellow Edesina fireballed zombie villagers and Seanchan soldiers alongside Green Joline. ALL Aes Sedai must be able to fight.

The ability to control one's emotions seems like it would be important for someone who is using psionic/mystical powers. However, this training hasn't seemed to be particularly useful to the Aes Sedai in the book since almost all of them seem prone to fits of various emotions. The rules are a way of shaping a woman to act in a certain way, thus the test tests both composure and battle skills. The Aes Sedai training seems to be about hiding emotions, rather than truly mastering them, which perhaps has been a source of some of the Tower's problems.

I would say that the emphasis on composure is arbitrary, while the emphasis on battle skills is not, thus the composure part of the test will become less and less important as Egwene expands opens the tower to more and more woman channelers.