rambling cang qiong mountain sect head canons
Liu Qingge is the WAR GOD. I think way too much is made of him being a "Bai Zhan brute" and a "sword-swinging uber".
That's Shen Jiu's dismissive and biased POV and Shen Yuan's affectionate and biased POV.
What his real role in the world is is tied to being the War God.
I think the peaks numbering system is just the order they were founded/a peak lord first took over a new peak and started a specialized branch of the sect, not the actual ranking of them in heirarchy.
And there absolutely is heirarchy.
I think Cang Qiong actually functions on a tier system more like an imperial court - Qiong Ding is the first peak and acts as the "emperor", making sweeping decisions about the sect as a whole internally and externally. Who they are allied with or going to war against and which peaks are assigned what role in a situation are decided by Qiong Ding.
Second are Qing Jing and Bai Zhan on equal footing.
They are the strategy and tactics peaks respectively, and each essential to the sects main function aside from cultivating to immortality - doing battle.
The wiki numbers them based on how the known sect leaders address each other as shidi/shixiong, which I think is a fair and accurate enough way to do it. Given no real solid information about their ages aside from Yue Qingyuan is older than Shen Qingqiu - and age likely not mattering so much to immortals - them organizing themselves based on seniority of when their peak was founded is perfect imo.
It seems logical that Qing Jing came first - that the initial Cang Qiong sect based on the Qiong Ding peak maybe had someone who was a skilled warrior that could have branched off to found a new sect, but decided to stay, but also needed space. This mysterious past cultivator founding a semi-sect on a nearby peak of the mountain and remaining filial to Qiong Ding to split the difference works as a precedent for this happening 10 more times. So they take over strategy and tactics and the 5 arts so Qiong Ding can focus on diplomacy more as the sect grows.
So when Cang Qiong goes to war, Qing Jing handled strategy and tactics, helping guide the other peaks military and cultivation power.
Wan Jian came next - a natural outstretching of them getting more disciples but not needing more leaders. They're the sword peak. They make the swords for the sect and act as infantry in war.
Then of course An Ding is founded. The sect is getting big and complicated and very powerful. They need more than just one harried guy on each peak to handle logistics separately and probably at cross purposes ever-more-often, a whole peak of people to do that for the whole sect in a coordinated way is an easy solution.
Then we have two peaks with unspecified specialties. Xian Su peak being all female cultivators suggests both of these peaks were founded without military reasons in mind. Probably during a peaceful time period.
Then comes Bai Zhan. The sect is now actually rather enormous. Having all the strategy and tactics concentrated on one peak makes no sense. Maybe there's a big war to give the final push. So they branch that out with the new martial peak. They don't have a specialty primary outside battle like the other peaks - even Wan Jian is forging swords. Bai Zhan is for forging the most powerful warriors they can. Bai Zhan's Peak Lord becomes the War God of the entire cultivation world - the one in charge of on-the-ground tactics in battle, freeing up Qing Jing to focus on overarching strategy, and in the process making them equals who are often working in tandem in war.
Then naturally comes Qian Cao. With a dedicated warrior peak and the resulting increase in battles for the sect, a dedicated healing peak is necessary.
And finally Ku Xing, Zui Xian and two unnamed peaks. Again considering the named ones are the Aesthetic and Alcohol peaks, it can be inferred the other two are also peaceful. The sect has the greatest military might in the world now - they can afford to have a whole peak of people eternally meditating or forever drunken as near-complete dependents. Maybe the other two are branches off of An Ding like Bai Zhan was from Qing Jing and they're farming and/or animal husbandry peaks?
And then over centuries everyone got really, REALLY good at what they did.
So in the end the way Cang Qiong works is:
Qiong Ding declares war, Qing Jing sets the overarching goals for the war, Bai Zhan deals with how to get those goals, Wan Jian provides the numbers and weapons to enact those plans, An Ding makes sure they have all the supplies they need, Qian Cao makes sure as many survive as possible, and everyone else either protects the home front of Cang Qiong mountain or follows in line with marching orders.
This is clearly the perfect way for Cang Qiong to have come into military dominance over the cultivation world and kept it.
But it doesn't work with the concept of Liu Qingge as a meathead who can only swing his sword around or him as a kinda goofy uber that appears out of nowhere.
Why is he always right there? Why, despite bad-blood between them, did Liu Qingge and Shen Jiu spend enough time with each other to clash often enough to get a reputation for it? Why does he know where and how to find Shen Yuan all the time. Why does Bai Zhan often attack Qing Jing to test it?
Liu Qingge as a tactical genius who is also insanely strong in martial arts fits better. Liu Qingge who, as Bai Zhan's Peak Lord, has a defined role in the sect to keep track of and be near the Qing Jing Peak Lord to consult with him while out and about fits better. Both of those things snowballing into his more complex relationships with Shen Qingqiu fits better.
Qing Jing and Bai Zhan are like a pair of Mandarin Ducks when war breaks out, so at all times they have to keep track of each other and a working relationship of SOME kind so they can work together seamlessly when the time comes.