I think in these examples you cited the channelers lost their ability to channel, because someone else violently broke a weave (especially a shield) by them, while they were channeling. This obviously doesn't seem to be the "officially" precise stilling weave, but rather like a forced explosion of the ability to channel (in this respect rather similar to burning out). However, this form of stilling someone seems quite risky, because it requires that your opponent channels, and it probably might kill him.

I only dimly remember this, but doesn't Siuan even indicate that she was stilled by a circle of AS in a process that took some time. So, apparently the real stilling is a bit more complicated, because it's basically a very delicate "surgically" removal of the ability to channel.

Since Rand & Co. likely don't know how this exactly works (or e.g. Cadsuane doesn't want to give it away), it would explain why they don't do it.