A weave that might be useful in one context might not be useful in another. Variations of Healing without a Talent for Healing, for example, makes the weave worthless to another channeler.

I think we could also look at the ritualistic practices surrounding the Test for the Shawl. It seems that most of the initiates learn the more useful weaves during their Accepted period of learning. Yet many of the weaves they have to learn to pass the Test are said to be "useless" or of a limited value. It is possible that some of these worthless weaves, in another context and given the right situation, are useful. Perhaps one of the weaves they are taught was the sonar-creating one used by the Wise Ones - but since no pregnant woman is nearby to test it on, it doesn't do anything. Also likely, is that those weaves might be variations or weakened versions of older weaves - when Sorilea showed Cadsuane the Travelling weave, for example, it was so flimsy and weak that it collapsed before it could create an effect. It could be the case that a similarly weak channeler, trying to pass this weave on to a younger person or student, could only roughly duplicate the matrix needed, in which case the younger student has a weave that doesn't seem to work, and which they don't have the technique to use. The chances of that weave being passed on become very low compared to a fireball or basic healing matrix of flows.