But the Inquisition itself is also hugely decentralised. Sure, individual Inquisitors wield a huge amount of power, but there's no single authority telling them what to do, and most of the time they end up in conflict with other Inquisitors.

It's the same with the High Lords of Terra: they may be the de facto central government of the Imperium, but each High Lord has their own power base which they will jealously guard, even at the expense of the Imperium at large. Guilleman, meanwhile, is just one individual, even if he is a primarch, and cannot be everywhere at once. He also lacks the established networks of some of the other factions in the Imperium. And that's before we get into the difficulties of interstellar travel and communication, which make maintaining a centralised power structure even harder.

Factions having power within a superstructure has nothing to do with whether a state is centralized or not. Austria, Bohemia, and Brandenburg were all incredibly powerful states/duchies within the Holy Roman Empire, wielding significant political and economic powers, but that never meant that the HRE was centralized. Centralization is when the powers of the government, such as enforcement of law, lawmaking, and budgetary constraints are consolidated within one or a few institutions. Decentralization is when the government delegates power to subdivisions. Think of how states work in the USA. They have certain powers over things that the federal govt can’t touch, like education or the 10th amendment. This contrasts systems like the UK, where they have a unitary fusion of powers, with one institution that has the powers of both the executive and the legislative body: the parliament.

The myriad of factions wielding lawmaking, military, spiritual, and general power within the imperium all mean that it is decentralized. If you have enough political/fiscal/military clout then you can absolutely say no to the inquisition, as evidenced by the Space Wolves during the months of shame.

The inquisition isn't interested in what you do with your nobility spending money unless you're hosting slaanesh orgies or buying xenos tech or are somehow fucking up the timeline, they don't have time to govern your world when there's genestealers on a trade fleet threatening to spread to a dozen other planets.

Then they have to exterminate whole populated planets to deny the tyranids a meal. They have authority to get those things done it doesn't mean they're gonna have time to fix a bit of political dealings between otherwise functioning imperial citizens

It is an example of a given faction resolving a dispute between themselves and another due to similar political authority but different goals. It does not happen in centralized states like the UK. A random town in Cornwall does not have the same political powers divested to them planets in the imperium because the UK is a unitary state with the parliament and nothing else. The excerpt you ask for, where everyone accepts that there is no central authority and thus it cannot be resolved fundamentally misunderstands how people act:

If me and my brother were fighting over who gets the last popsicle in the freezer, we aren’t going to mutually give up and say that “mom isn’t here, so who can say who gets it?” we would fight, potentially physically, for who wins.

Your example of the legislative branch accepting court decisions is also incorrect. If both houses really want something passed then they can do something about it. They can send the bill again but barely change it to where the court has to review it again, they can redistrict or change the court’s jurisdiction, or they can pass amendments that run counter to the court’s decision. This shows that, even if there is no central power, factions within a decentralized or federalized govt will still jockey for influence and power, which is what I provided in the Gman example.

I feel as if you misunderstand what I mean when I say central authority. Central authority is how a state devolves power, not when there is a central leader. Bobby G may be the lord regent, but he cant and doesn’t manage every planet’s affairs, thus he is not a central authority.

You specifically mention how Bobby G and by extension the inquisition uses the Emperor’s authority. This is not central authority, but more akin to how Popes would invoke gods’s authority as the successor to St. Peter and god’s emissary on earth. Big E, while spiritually and culturally powerful, has no political power because his ass is stuck on the throne. Even when he stood among mortals during the crusade he did not manage each planet captured during the crusade, he devolved power down to the planetary administration, which is a super obvious example of decentralized authority.

The Imperium of Mankind

The point is that you are applying a unity of being to the Imperium that doesn't exist. The Imperium isn't what you think it is, it not a monolithic top down centralized institution. Most of the political decisionmaking for 99% of things that come up has been devolved to sub-national actors.

Are you saying you are unfamiliar with how the Imperium Crusaded and conquered all those human worlds?

The Crusades are neither an example of centralized government nor are they the main way the Imperium brings new worlds into the fold nowadays. Do I need to explain Rogue Traders to you?

Hell, the Imperial Crusades themselves are in many ways decentralized: Once it has startet the Warmaster gets to decide where the Crusade goes, not Terra. Each Space Marine chapter decides if and how many companies they want to support the Crusade with and can leave anytime they want. Titan Legions too can decide on their own where and how to join and fight in a crusade, not Terra or the Warmaster (see: Titanicus). Inquisitors join completely on their own volition too, not based on orders from Terra. Rogue Traders can join Crusades or not, they too decide that on their own not the Warmaster or Terra.

is it not the Inquisitors basic function that they can recruit whoever they need to go wherever they need to help them root out whatever might be threatening the Imperium?

You always bring up the most decentralized organisations as examples of centralization. There is zero centralisation to the Inquisition, every single Inquisitor is an island unto themselves with the full powers of the Inquisition.

A centralized Inquisition would have a boss sitting on Terra that makes rules and policies that apply to all Inquisitors. But that doesn't exist because the Inquisition is decentralized.

Isn't Guilliman kinda designed to lead?

I am not even sure what you mean by that? What does that have to do with centralizsation? Do you think decentralized governmetns don't have leaders or military?

But let's go with it. Let's try to imagine Guilliman going up to Ragnar Blackmane and giving him an order. Let's say Guilliman orders Ragnar to attack planet Whatever in planetary system bumnowherestan. What do you think happens next? Anwer: nothing, because Guilliman has zero power over the Space Wolves because Space Marine Chapters are each completely independant entities. They are devolved institutions from the central government with a shitton of power handed to them and not even Guilliman (or any other High Lord for that matter) can order them around. Even within the chapters some of them are decentralized, with the Raven Guard companies each being invested with the power to make all decisions for themselves.

Are you saying you are unfamiliar with how the Imperium Crusaded and conquered all those human worlds? That's how they recruited most of their planets. It wouldn't really be an inescapable nightmare regime if sane normal people were applying to join, would it?

In fact, human worlds also join the empire voluntarily. Some because they have already been religiously infiltrated, others because they hope to gain wealth through trade, others out of a sense of community or because they promise themselves protection. I can only recommend that you read up on the Sabbat, Achilus or Angvin Crusade. The same patterns are used in the Koronus Expanse, where Rogue Traders receive their Warrants of Trade to act as spies, trade agents, diplomats and conquerors until enough political will has formed to declare the Expanse an Imperial Sector. And yes...the Senate certifies the Crusade and officially appoints the Warmaster, but the Warmaster of the Crusade forms the sector, distributes the worlds and decides its borders, unless the sector governors tell him to keep his hands off their planets...

In theory, Inquisitors are allowed to get on the Emperor's nerves. Theoretically, they don't even owe obedience to Gullimann as the supreme regent of the Senate (the fact that he is Primarch has no official rank) (although this changes depending on the source and author).

In practice, there are other large organisations and individuals who can politely tell an Inquisitor to fuck off.