Thats actually an excellent point that I have never thought of before. The good guys dont need LTT in Rand's head, they already had someone with all the knowledge in Birgitte.

Could you imagine the rage if Mat met Birgitte in the next book and introduced his new gunpowder&cannon invention only to have Birgitte go "oh yeah, I knew about that. This is how you can improve on the design and make them far more lethal. What? Why did I never tell you this before? Well, I guess I forgot."

Or better yet, now that I think of this, why is it that it did not occur to Nynaeve for instance to ASK Birgitte how to seal the DO away properly in one of her meetings with Birgitte in the world of dreams. I mean at that point she still had full access to her memories and would presumably remember earlier turnings of the wheel.

Or just have Mat blow the horn and interrogate the dead heroes. Hawking would likely be happy to instruct Rand on how to win. The shadow could be defeated in time for supper.