>>9758You are thinking about it too abstractly
No, the inquisition couldn't go to war with the entire imperial guard to assert its authority, it doesn't need to, that's not how it as an organisation works, that would be a bit like the CIA trying to go to war with the entirity of the US military
The two organisations at the higher echelons co-operate more readily than the ad-hoc haphazard way individual inquisitors interact with Imperial guard army groups or regiments
The way the very top most levels of the imperial heircharcy actually work on a day to day level is deliberately left vague both because the setting really isn't about that, its about fucking shit up with big guns or at least it was for most of its life, and to grant individual writers flexibility
Everything in the imperium is a delicate bullshit balancing act by design to prevent any one part of it being able to rebel and take over, after the Space Marine legions split and dragged the imperium into civil war the last time
So the Galactic civil administration is completely divorced from the army despite providing it with supply and financing and the army is divorced from the navy despite relying on it to get from place to place and the navy has to go to the Adeptus Mechanicus for ships who are like a weird empire within an empire that don't really answer to anyone else even the inquisition but they need the rest of the imperium so they begrudingly build everyone else equipment and talk to the Merchant Navy who are related but seperate to the Military navy to get it distributed to the Army and the Navy based on contracts sent by the administratum that due to all the extra layers of deliberate obfuscation and the massive size of the imperium and the fact that the people that the contracts are for probably don't get any input into them are usually stupidly inaccurate
The Imperium basically has no central government on the galactic level, its individual planets/systems united under whatever their local govermental model happens to be with 5 or 6 big Intergalactic monolith organisations and a few hundred other smaller ones kind of loosely holding the whole thing together with no guiding administration overtop of them anymore
The inquisiton fits into this by basically being the archetypal glow niggers, they get by on excessively shady bullshit and a licence granted by GOD himself (he's not a god though shut up that's heresy against GOD, or maybe it isn't depending on what planet you're on) to do what needest be done, whether that's sacrifing 15k soldiers to secure an alien artifact or executing a loyal citizen to get a hold of his business to secure more capital for yourself, they gain their funding partially through being granted part of the Imperium's taxation by the administratum, partially by just directly requisitioning whatever they need and calling in favours and partially from having their fingers in every pie worth poking in the imperium, being six hundred years old with above top secret knowledge of the political and economic spheres of the imperium and probably also having psychic powers do wonders for your investment portfolio
But TL:DR, the setting is deliberately vague at the ages, more space fantasy than scifi and is designed to be unpleasent, stupid and chaotic, the imperium is the most bloody and uncaring regime imaginable, per the opening text, at the Macro level everything is stupid and awful for comedic effect, so don't sweat small stuff like economics