There's a part of me that has always wanted Chaos to be a bit more of an... Anti-Imperium. Of course all of the evil, torturous demonic shit happens but... hell some of that happens in the Imperium, too like throwing a thousand souls a day at the Golden Throne and servitors and what not.
But like, I would love to see Chaos emerge as an even-more-forceful worship mill for its patron god, but with some actual organization to it. They're essentially trying to do the same thing as the Emperor was... expand out, rule everything. The Chaos gods are just doing it specifically to rule everything and enforce worship to increase their power.
There has to be SOME form of organizations, though. Things like the Dark Mechanicus exist.
With the nature of the Warp, making Chaos an Anti-Imperium would always be problematic. Most interpretations of the Warp as being screwed up when it comes to time and the Warp being described as an ocean with currents, storms and tides and the like, with the figurative water replaced by literal emotions and souls, and the obvious time displacement that occurs (ie Abaddon's 13 Black Crusades are a weekly event, the Abyssal Crusade Survivors emerged almost a millenia after heading into the Eye of Terror and destroyed 400 Chaos Worlds in spite of a huge increase of Chaos Incursions from said Eye of Terror happening immediately after said Abyssal Crusade was launched, and worse the idea that Slaanesh always existed... but also never existed according to the other Chaos Gods). It's hard to make a functional society like you'd have in real space, if time and space don't follow the rules they do in real space.
Along with time not working well, space doesn't either as the Chaos Gods can manipulate and warp (no pun intended) things on their Daemon Worlds to some degree. Chaos Corruption can do horrible things to people in the material universe, imagine such distilled corruption occurring constantly unfiltered in the Warp.
With that said there is obvious organization. And there are hierarches. There are Forgeworlds in the Eye of Terror (and in the normal galaxy as well) as well. And if the Chaos Gods want a world to be "normal" as you say, they can be so, and there are "normal" worlds within the Imperium. They're mentioned in things like the Black Crusade sourcebooks. And the organization overall is dedicated to bringing more worship and power to the Ruinous Powers actually so your not wrong on that point. If there wasn't any organization towards certain purposes the nigh infinite number of Daemons in the Warp could just likely murder all of the slaves, worshippers, cultists, Chaos Space Marines etc but they don't because they are following their respective Gods will and desire.
The other problem with making an anti-Imperium, beyond the lack of following time and space is that you have Khorne whose dedicated to the most extreme excesses of martial prowess and war mongering which means a lot of fighting and bloodletting all the time, Nurgle whose all about decay and disease and blooming life via plagues and rot, the perpetual hedonism and excess party that is Slaanesh to the point that they're so dulled by centuries of empty pursuit of pleasure their primary drive is finding new depravities and stimulation, and Tzeentch who... well... the big bird seems fine. I can't see why you can't make a stable society out of backstabbing, cunning, manipulation, trickery, guile and illusion. That's basically a political meme I feel.
Ultimately... in the Warp I don't feel there's any real advantage I feel, in just making an Anti-Imperium... unless your just engaging in some sort of Tzeentch level psychological mind games, or using it as a testbed for things. Having "normal" crapsack Chaos dominated worlds in real space could make sense because... that's what works there. In the Warp... no need to be constrained by normal reasonable expectations.