Short answer: If you are looking for brotherly or sisterly bonding in an organization, you may be looking in the wrong place.

I think you may be overlooking the interactions of Mat, Perrin and Rand before the quest started in earnest, Beslan Mitsobar and his relationship to Mat and Thom and Juilin's relationships. There has always been brotherly (and sisterly, looking moreso at Elayne, Egwene and Nynaeve) bonding.

For example, "the first hint of trouble" you refer to revolves around one of the three main male characters becoming the Antichrist that will apparently go insane and destroy the world. Plot convenience aside, that is some pretty scary stuff to have to deal with especially confronted with the idea that your friend actually does have those powers, and I think it comes down to the idea that this is a childhood friendship that quite frankly would never have been tested to such a degree so early in these characters' lives, so some of their communication issues are understandable.

It just comes down to the fact that organizations backed up by military force or political clout are so institutionalized that they easily lose track of the belief systems that united them in the first place - The Aes Sedai, The Black Tower & The Children of Light share more similarities with each other than the relationships that develop around and between individuals.

Part of the success of WoT, after all, is that it is so familiar to readers and parts of the worldbuilding are based on real life rather than more fantastical elements.