... and I agree that the greatest benefit in a mixed circle occurs when the two halves of the OP are woven together. But I still have the impression (despite your arguments) that there is some benefit even when the two halves aren't woven together.

I'm still not sure about what the leader can do with the OP she's accessing through the other members. I agree that it's not passing through her, as you said. But I still think she doesn't have to utilize/weave any of the power she's drawing through other members, if she doesn't want to. I think she can just let it dissipate back into the OP pool, essentially.

Consider when Elza obliterated Osan'gar at the Cleansing. From the wording of that scene, it seems she only used the saidin she drew through Narishma and Callandor, even though she was accessing saidar through Merise at the time.

Also, consider Rand at the Cleansing. He used saidar and saidin completely differently - he never combined them into a single weave. And if he could do that, it would seem he could have chosen not to do ANYTHING with the saidar he was drawing from Nynaeve, also.

But your argument - that the leader can't help but use at least a very small portion of the OP she has access to through each member, when weaving - actually explains the general impression I get, that there is ALWAYS some advantage to being the leader of a mixed circle, in terms of the potency of the weaves generated. That is, because the leader has to draw & utilize at least a small portion of the OP from each member, the resulting weave will always have at least a small mixture of both halves of the OP, and therefore will always result in a more potent result compared to if only the same amount of one half of the OP was used.

Whereas, I was trying to explain that general impression by suggesting that the leader gets some Precision advantage from the mixed link regardless which power(s) he/she uses, and from which members, in any particular weave. Despite your arguments, I'm still not convinced I'm wrong about that. But, I could be.