Maybe that was the point, or at least part of it. The WT is supposed to be a significant authority in the Westlands, but it's fallen a long way from the height of it power prior to the Trolloc Wars. Maybe it's part of one of the overall themes in WoT that humanity in this age is weakening and dwindling, not just nations have been failing since the time of Artur Hawkwing, but we see it in the WT too. The number of sisters has fallen, their ability to wield the OP has lessened, this whole theme is mentioned in the main series a few times, and even more strongly in NS.

It's probably also supposed to be a result of Rand breaking the world. Look how many nations have been ripped apart by civil wars and internal discord simply because Rand is. The same thing happened to the Tower itself, especially when there are several influential Ajahs with sharply opposing world views and simmering animosities that have been brewing for many years.

And don't forget the role of the FS and BA. We know Alviarin (and probably the other leaders of the BA) was under direct orders from the Forsaken to break the WT. It's obviously no coincidence that she helped Elaida instigate the whole mess, and I'd imagine important BA sisters in the Blue like Sheriam and Moira didn't just flee to Salidar in a snit over Elaida, but may very well have been following orders from Alviarin or even Mesaana. A reunited WT is a blow against one of the DO's schemes to sow chaos.