Everything whithin the state, nothing without the state.
The chancellor is the personnification of the confederation. For various reasons the Liaos are the chancellors (though I point out that from memory the confederation has been happier with "non-ruling line leaders" then other successor states). It is inevitable that having a "cult", which could easily be in a light sense, like parading once per month with an effigy of the chosen one, around a human being is easier to understand then a cult towards vague notions of an all-encompassing system which ends up having an aristocracy anyway. Two kinds of 'em to boot.
But that's basically it, there's a difference between deifying a distant leader in a state cult, and TRUELY considering him as god incarnate. There's a difference between deifying a man and having a cult to him, and being bound to the state. The man will be replace, people come and go, but there is no existence if there is no state.
Another illustration regarding de deification of the last chancellors (which had never been a thing before): Think of old polytheistic religions in the more philosophically bound societys of antiquity. The religion was, not completely but still mostly, a "state cult", not a "religion" as we tend to comprehend the word. Much the same, in the middle empire, while the emperor weilded the mandate of heaven, he could be replaced in a moment's notice and his subjects would merely look forward to the new "coronation festival".
The chancellor is the personnification...but only that. He is still subordinate to the state in theorie. Hence why the chancellors prior to Romano were all very keen in re-interpreting the Korvin doctrine, the Sarna mandate and the basic tenets of warrioresque filial piety, I mean the Lorix Order. The chancellor is but a man and while the theorie behind the confederation has been tempered with in time, history is not necessarly forgotten.
I mean, which warrior house was the most eager in upholding the ideas of the Lorix Order? The same that was considered less reliable then the others.
The Sarna mandate enabled a resurgence of the nobility. Then during the reign of Tormax, through re-interpretation, it allowed to curb their growing influence.
A state cannot stagnate for too long. Its policies evolve.
Now, let us consider something of the inner workings of the confederation. Maximilian managed to find enough dissent among the ruling caste to make a coup against his father, the ruling celestial wisdom, and install his people in most key positions of power in the confederation without anyone saying anything and with, for all we know, minimal blood shed with only higher ups being liquidated for replacement.
Following the coup, power struggles were constant. It was not necessarly attempts to grab power on an purely individual basis, not necessarly attempts at gaining more prestige for one's aristocratic line... But power struggles were very real. Warrior house against CCAF, Death commandos against Maskirovka, and everything in between...
Now the fallout of the 4th SW enabled Romano to clean house as well as definitely crushing the power of (at least) the Sheng nobles, notably with a great deal of nationalization of the economy (I seem to recall there were contradictory entries on this subject in the handbook though)...But Sun Tzu undertook steps for a certain liberilisation of society and economy.
Then, I remember clearly all those passages in "the capellan solution" where Sun Tzu is always carefull to keep his inner circle divided...assuredly for he knows that his position as chancellor is that of a god, but mewrely an embodiment of the state, and that he is not the sole individual capable of playing this role, as capellan history shows.
And then you have the prefectorate and the linked house of scions, the power of which has sometimes been quite strong....to the point of naming the most incapable chancellor in the history of the CC if I recall.
Inner power struggles are not really the main draw point of the BTU and hence only show up as needed...but inner power struggles are rarely things that are shown in broad daylight until they are ready for it, or coerced into action before they reach their maturity. It's far from impossible to do something with all this. A Civil war, not with thugees, but between traditional elements of capellan governement, could be quite the epic tale. Not likely to happen, sure, but a potential epic tale nonetheless. The death of Daoshen could put several things in motion, espescially if it coincides with a defeat. It would be ridiculous that so many powerfull entities would be happy with the curtailing of their prerogatives since Romano Liao to keep foolishly smiling ever after, even through defeat. When your nation is winning...can't argue with success, but defeat opens another realm of possibilities.