The White Tower's Strength Hierarchy is not a Problem
I know, it seems like a hot take that has to be a shitpost. The idea of a person being in charge based solely on a physical attribute beyond their control makes monarchy look like a good idea. But I don't think it's actually what the system is, or the intent behind the strength hierarchy.
Basically, most of us completely miss the point of the Aes Sedai and the White Tower. We keep seeing them as an institution of a particular type, like a military or a government or a religion. But it's not. It's a union. Its purpose is to facilitate channelers, like a union's job is to advocate for, and protect, workers. And the part of a worker's life and attention dedicated to his union, or even his job, is only a part of what makes him who he is. Yeah, it influences a lot, like his status in life, where he lives, who his friends are, and so on, but at the end of the day, you work to live, and no matter how staunch your membership in the Local #whatever, you're going to be more worried about getting your work done and going home to your family, your interests and your hobbies.
The Aes Sedai are not soldiers in an army, or bureaucrats in a government, or clergy in a religion. They are not even soldiers, security forces, scholars, philosophers, doctors, diplomates and activists, depending on their Ajah. They are heroes. Protagonists, each of an adventure story. Each one is a powerful person who has an agenda they want to see done for their own advantage or the benefit of others, or just because they want to. The Tower and their Ajahs are just things they sign up for to get that done. Yes, the Tower engages in geopolitical shenanigans, but that has as much to do with what each sister does, day-to-day, as a country's foreign policy does to everyone who is not abroad, near the border or on the internet at the moment.
Basically, every given sister's job at any given time is what she thinks it is. Some of them need or want to be told what to do, so they pick "serve the Tower" and hang around to be given assignments. Others lock the door to their study and yell their cultural equivalent of "fuck off" when someone tries to assign them duties, or just head out into the world to do what they want. And that's cool with the Tower, however annoying a particular Tower authority figure or faction thereof might find it at the time. Because that is what the Tower is for, to make it possible for them to do that stuff. That is the essence of empowerment, and that is the Tower's purpose. They train you to channel, give you an excellent education, train you how to push around deal with people, pound into your head the importance of making a good impression and set you up with unlimited funds, and sit back to see what you do with it.
The problem is, people are going to people, and eventually, each sister will realize that the biggest obstacles to doing what she wants are her fellow sisters. The point of the White Tower is to govern those inevitable clashes, and sort things out, not to achieve some platonic ideal solution, but to minimize the drama and not let the world take advantage of the conflict or distraction. If Aes Sedai are too busy butting heads with one another, some damn fool male might start improving international cooperation and establishing schools that gather a critical mass of scholars and technicians to jump-start a technological revolution might screw everything up.
But that means, there needs to be a rule for who wins, and who gets her way. From the Tower's perspective, it does not matter who wins, so long as there is no fighting over it. The Tower is basically a parent, and every single woman with a Great Serpent ring (or, honestly, the ability to touch saidar), including the Amyrlin, are the kids. As a great comedian whom we should probably be grateful never had access to actual forkroot would say, "Parents don't care about justice, they just want peace and quiet."
From that perspective, the strength hierarchy is an excellent rule. There is no way to game the system, you can't legislate to change it. And like Tic-tac-toe (and Global Thermonuclear War) the only way to win is not to play. Don't like the idea of a woman giving you orders just because she was born with higher innate strength than you? Don't get involved with her! That's all there is to it.
And we see there are many, many ways to get around the strength hierarchy. All you really need is to not require every single person on the planet to give way to you. The Hall and Amyrlin had an plan for Moiraine's career and the authority to make it happen. That's why Moiraine begins the series on the Sun Throne. Oh, wait. No. How did that happen?
Because she is an Aes Sedai with all the power and resources her White Tower training gave her, and the self-awareness to say "Nope," and skip out to do what she wanted/thought was more important. She ran into Cadsuane, too, who also had ideas about what she should do. Didn't take, either.
The main place in the story where it seems like the strength hierarchy messes things up is with the rebel embassy to Rand in Caemlyn, where Kiruna and Bera march in and take over the embassy and head off to comeuppance at Dumai's Wells. You know whose fault that was? Not the woman who first proposed strength as a criterion for situational authority, but Merana. Because she let their strength, or Verin's experience before that, matter. And that was mostly because Merana didn't really believe in what she was doing. She knows her authority does not really come from the White Tower, only a pack of cranks in a village. She is there to serve the agenda of the Salidar rebel movement, and deep down inside, she knows they are there as supplicants to Rand, trying to get him on Team Salidar. She is not there trying to save the world through negotiations, she is just working for a petty factional grudge. So on one level, she knows she has no right to assert her Hall-granted authority, and on another level, she isn't certain that Verin or Kiruna & Bera don't have a better idea of what the best interests of Salidar actually are.
Another major loophole we see in the strength system is cooperation between sisters. Delana, when she is thinking solely as a conventional sister, before she is refocused on her Black duties, notes how Siuan once protected her in their friendship and now she has to be the one protecting her. It's not Delana mistaking their respective strengths for competence to protect one another, it's Delana acknowledging the strength system, and meaning that where Siuan once prevented women between her & Delana in strength from bossing around her Gray friend, now Delana is going to be protecting Siuan from being bossed around by women weaker than Delana. We see this in action with Cadsuane and Daigian & Kumira. Cadsuane respects their mental abilities and judgment, and from their perspective, what more do they need? Rather than claw their up through a meritocracy and securing their position based on some esoteric algorithm weighing the value of their specialties, or pushing their ideas through a review and assessment procedure, all they have to do is convince Cadsuane. And then Cadsuane will see to the implementation of their ideas, or prevent other sisters from interfering with them on the basis of strength.
For a more equitable version of such an arrangement, we have the relationship between Nynaeve & Elayne. There are no two Aes Sedai with a PoV in the series with as much respect and trust for one another as these two have. And we see a few interesting examples of how they work with the strength dynamic in WH.
The first is when the issue of the damane captives who want to have the leash removed is broached to them. Elayne has an opinion on the matter, but she lets Nynaeve make the call because she is the strongest women around. But Elayne is willing to stare down Birgitte, a hero of the Horn, over the civil rights of a man they are certain is a murderer. Is she really going to let Nynaeve keep damane enslaved? Nope. She is letting Nynaeve make the call, letting the system stand, because of her absolute trust that Nynaeve will make the right call. She has been working closely with Nynaeve for over a year now, and most importantly, she saw how Nynaeve handled a related situation in the disposition of the two sul'dam they had captured. If ANYone was going to know that Nynaeve was going to get it right, it would be Elayne. And no, Lan is not telling her what to do, he is speaking to the world at large, he is offering his own opinions based on being in a very similar position, and that's why his own congratulations of Nynaeve for her decision affects her so much. And I think the Kinswomen were feeling her out with the question, because they are worried about ending up in a similar position as the damane, vis a vis the Aes Sedai. Their own agreement with, and pleasure over, Nynaeve's choice speaks to their feelings on discovering that the White Tower (embodied in that moment by Nynaeve) has the right values, and they can trust it to take them in again, without abuse. So what is the point regarding the strength hierarchy, if everyone involved was in agreement on this issue? By referencing the hierarchy, they are not just a bunch of women who happen to have the same opinion, they have made policy, by following institutional procedure, and that gives their agreed-upon course of action weight and it strengthens the connection between sisters, Kin and ex-damane.
The next example is when, after Elayne's near-assassination incident, Nynaeve starts lecturing her and Elayne tells her that she does not want to disobey her, so don't try to use her authority. She's not dismissing Nynaeve's authority, she is respecting it, but also saying that she thinks this is more important. And Nynaeve realizes this, and does not flex on her. Because with reasonable people, self-evident situations like this weigh more that artificially imposed definitions.
And finally, in their last shared moments on-page in Jordan's lifetime, Elayne realizes that Nynaeve is up to shenanigans, noting that it has to be something really out of whack if she's hiding her plans, instead of flexing her strength position. Which incidentally speaks to Elayne's trust that Nynaeve would not abuse her authority, and also the point that she does trust Nynaeve, regardless of how crazy her current scheme is. Or at least, she has a guy to bond and bone and so she'll let Nynaeve do what she thinks she needs to do. Later on, when Rand indicates he sees through her own façade, and knows she has something she is trying to hide from Nynaeve, if not the bond-and-bone specifics, Elayne has a moment of chagrin, because if this guy whose experience of her is basically three days of dating saw through her subterfuge, her partner in crime comrade in arms of far longer standing should have, too. And the answer to why Nynaeve did not interfere is the same as why Elayne picked bond-and-bone over solving Nynaeve's thing: they trust each other.
If you have trust, you don't need to worry about who is ranked higher, and the system cannot stop you from ignoring it and building that trust with other people. And by being so clearly unfair and onerous the system is all but demanding that you reach out to your sisters, and build trust between yourselves, so that you don't have to be constrained by the idiocy of who was born with greater strength in the Power.
And if you can't build trust, stay out of one another's way. Either way, it keeps the White Tower from falling apart and Aes Sedai from internecine conflict.
In the end, it was not the strength system that failed the White Tower, but the formal hierarchy, with its elected leadership and ostensible selection of authority positions by merit, of which the Blue leadership boasts in New Spring.
And for all that the Wise Ones are hailed as a better system using superior criteria (though my own issue with that one is 'who decides who fits those criteria best?' and we see through Perrin's eyes on the conflict between Amys & Sorilea in LoC, it's not always so simple), as an institution, the Wise Ones lied to their people for 3,000 years, made them vulnerable to Couladin's pandering demagoguery, and failed to contain Sevanna's lateral thinking. When it comes to practical results, the Wise Ones are not noticeably more successful than the Tower.