One: Why would the Tower restrict themselves to the middle? They won't stop anyone who is too strong from joining them. But they do stop people who are too weak from joining them. 37.5% of all channelers, in fact.

The truth is that Sharina isn't representative of the majority of channelers who are never found. For every one Sharina that is found, there are hundreds of Kin or other women who could learn, who are WEAKER than the average Aes Sedai. There are only 6 women stronger than Nynaeve, but there are thousands of female channelers. So people of that level are simply very rare, and VERY far above the average woman in strength.

There is no sensible reason why the White Tower would restrict stronger channelers from joining them. The reason that Cadsuane is the strongest modern channeler, is because a woman of her strength is exceedingly rare. Not because the Tower are deliberately excluding stronger channelers. But they are deliberately excluding weaker channelers.

I challenge you to provide a mechanism by which stronger channelers are excluded from the Tower.

No, logic says someone like Cadsuane is far above average strength.

Two:

Even if, as you suggest, Moiraine is close to average strength, that means that Moiraine is above 50 in strength. And since we know that Egwene is stronger than Moiraine and Melaine combined, that means Egwene must be at 100 strength or more.

That means Egwene is stronger than the strongest woman, Lanfear, who is at 100. How do you explain that in your quirky model?