IIRC, anyway. I'm pretty sure Rand and some of the AS have mentioned that tying off a weave makes it easier for the enemy to break, whereas actively maintaining it makes it harder for the enemy to break or circumvent.

And making a razor-thin air blade and slicing around with it might work, but not necessarily that well. Weaves tend to lose their edge as they're used and the edge has to be constantly re-made by the channeller to keep it sharp. I doubt it would work on a battlefield unless you could get the enemy to hold still while you chop them, and I don't think even Rand is strong enough to hold a miles-wide battlefield still with air.

Anyways, all that said, there are still definitely better weaves than the same tired fire-and-lightning business that they seem to go for so much. Maybe it's just a matter of Taim not teaching anyone loyal to Rand how to do anything worth doing.