Every channeler? What particular Talents or skills have Terava, Someryn, Mesaana, Tamela, Viendre, Meilyn, Kerene and Edarra shown? We've spent a reasonable amount of time around some of these women. And I'm not saying they are devoid of skill or Talents, but what particular ones of theirs makes you say everyone above Moiraine is very skilled and has many Talents?

The fact that he was a Forsaken is some indication, no? The 13 that survived were the best, for the most part, with internal gradations. You don't get to be Forsaken if you have no skill.

No, since he's the one who mixed in the TP as well. Unless you think he invented and created ter'angreal to use the TP, which only means he has a different skill set.

Any of the Red Belted Kinswomen, Suana, Dagdara... need I keep on?

And the major character thing isn't a cop out. Because if I were to restrict my sample to that, I can also claim that no one who is ugly can channel great amounts of the OP. Looking at just the same characters you are, can we conclude that either being a strong channeler makes you good looking, or only good looking people can channel large amounts of the OP.

I'll match your meaningless caveat too. I see a trend, not a rule...

What is the connection to strength in the OP, here? First of all, only 9 sisters in the entire Rebel camp could make Cuendillar. If the majority were Yellow, the sample is still too small to make conclusions. But even ignoring that, who said these Yellows were strong in OP strength?

The very best at making Cuendillar, Egwene and Leane, have little to no Healing ability. The Companion even says this outright:

So what point have you proven?

Precisely. The only thing that mattered was practice. Not some innate ability. Talent lets you skip the need for practice, but barring that, skill only comes from practice, not as a side benefit of being stronger in the OP.

Only when the battle was restricted to a pure strength duel. She copied Egwene's weave against Amico, and Modhedien's weave to stop it. That's all. There was no extraordinary skill at play here.

As does every single other Aes Sedai we see. Meidani, several levels below Alivia, picks up Traveling instantly. We see Asha'man of a wide strength range copy Rand's Blossom's of Fire right away. We also see how the moment Nynaeve does her Healing of Siuan and Leane, a host of Yellows of a very wide strength range pick up on it right away.

It seems to me that once you've practiced with the Power enough, copying a weave is routine, so long as ability isn't restricted by strength in a flow, or the requirement for a Talent.

This is both ludicrous and false. Cadsuane did not say "so you see and copy". Cadsuane says:

There is no indication that Cadsuane is surprised that someone who watches can copy a weave.

Uhh.. WHAT? Are you insane? Cyndane used her superior skill to not just match a woman much much stronger than her, she handily beat her. Alivia ended that fight with her hand broken and burned to the bone. Even if Alivia had held her own, it doesn't mean strength is "a type of skill". Because if Alivia had Cyndane's skill, she'd have finished her easily.

Even with a sa'angreal Egwene would be no better at Healing. They use angreal because you can use more of the OP that way, and also because you get less tired if strength comes from an angreal rather than yourself.

There's also memories leaking from Lews Therin, there, completely removing Rand as a reasonable candidate for this discussion.

And also linking stronger channelers to good looks, and a whole host of nonsense. The sample size is too small, and too cherry picked.

This is hardly the same. See, height has a causative relationship to reaching the lightbulb. That this is so is proven.

You are claiming a similar causative relationship between strength and skill, despite the Companion flat out contradicting you, and nothing at all in the text saying this is the case.