Let us consider that for a very strong channeler, who has already learned to split flows and has no trouble learning weaves, that the test for the shawl would require an additional aspect to make it truly challenging for them. I think we can all agree that at this point, Nynaeve, Egwene and Elayne could pretty much pass with very little effort if all that was required was to weave memorized flows while handling things like trollocs and such. Pfft. Cake, for our girls.

Thus I submit that it must be that the psychological component to the test is cranked up to crisis levels when someone who is very strong in the Power is testing. The stronger the channeler, the tougher the mental and psychological aspects of the test become. It is well known that amongst the sisters strength in the Power is often equated to strength of character and leadership ability - we also know this to be a flawed system, as we have examples such as Elaida and Alviarin, who show us that while you can be strong in the Power, you can also be emotionally brittle, easy to manipulate and weak of character; and we have opposite examples, such as Siuan, who is now weak in the Power, but is mentally tough, virtually impossible to manipulate, and very strong in her personal character. I digress.

Since this is typically the way the sisters organize their hierarchy, it would make sense that they would throw more mentally traumatizing scenarios at those testing who are strongest in the Power, thus determining immediately (and privately I think, the information likely being "restricted" to those administering the test and the Amyrlin) whether or not the Accepted being tested is actually as mentally strong as they are strong in the Power. Wouldn't YOU want to know? I would. It would be a very handy piece of information to have, knowing that the sister next to you might be an extremely strong channeler but would crumble under, say, political stresses. You would know exactly how to manipulate her, what level of strain she could stand, and for all intents and purposes, use her own strength in the Power for your personal use. Handy dandy. And you would know the moment she gained the shawl, IF she gained the shawl.

It's just my personal feeling, but I've always felt that there was a missing component to the idea that the sisters would bow to whomever was strongest in the Power. This gives more depth to the notion, for me.