Wouldn't the Emperor's plan fail since the Imperium is brutally fighting xenos, daemons and heretics and by doing it feeding Khorne and making him stronger and stronger? Let's say the Imperium would defeat all enemies and Khorne somehow weakens, then Nurgle would feast on the decay and regrowth. And humanity will keep being curious and there is Tzeench at work, let alone lusty enough for Slaanesh. Is there any proof that the Imperium's efforts were worth it?
What plan exactly are you talking about here? It sounds like you think the Emperor's plan was simply to conquer the galaxy and overcome all enemies, including the Chaos Gods, by force.
That is not so. The grand plan was to build a human-controlled Webway, a means of interstellar travel that does not require entering the Warp. This would starve the Chaos Gods because the Warp is their home and the true source of their power. Things like bloodshed, lust, curiosity and decay give shape to that power and make humans vulnerable to it, but without contact with the warp, they would not be an existential peril, and mankind could develop its Psyker talents without the fear and threat of Chaos.
Alas, the Webway project failed due to the treason of Horus, and the mortal wounds the Emperor sustained have basically forced the Empire of Man to improvise and constantly fight for survival ever since, often resorting to desperate and self-destructive measures.
They may be feeding the very power they are fighting, but what else are they to do? Just give up and accept the inevitable? That is not the nature of mankind. As long as there is hope, we fight.
And there is always hope.
The Emperor came quite close. If Magnus had not destroyed his work in the webway, the Emperor would have effectively eliminated humanity's dependence on the warp. Control of the webway would allowed instantaneous travel across the galaxy and would have made psykers (astropaths and telepaths) redundant. Their subsequent extermination from the gene pool would leave mankind nearly impervious to Chaos' common vectors into the material universe.
I think what's being lost in this question is that the Emperor's plan wasn't just the Great Crusade. Sure, he wanted to establish the Imperium and stretch mankind's dominance across the stars. But this growing empire, like the Primarchs and everything else he created per-Heresy, was so that the Emperor could put his final plan into place. The Chaos Gods genuinely feared his plan and while you can say the Golden Throne's defeat was inevitable, I think it's fair to say that Chaos pulled out all the stops to stall the final capstone on the Emperor's master plan.
- Emperor uses chaos to gain power (Primarchs),
- and then retires to build human control of the webway,
- but his tools for the crusade are corrupted via their ignorance of the Emperor's true plan (because he trusted no one with a full knowledge of Chaos)
- and ultimately this ignorance fouls up the final part of the Emperor's grand plan to liberate humanity from Chaos' grasp.
- Quite honestly it is a lost cause.
- The Chaos Gods are not governed by rules like we are.
- Humanity is so far behind in the race for control that we never had a chance.
- The Chaos Gods have, and will continue, to intervene when there is a threat against them.
- Though humanity is doomed against Chaos, the added threat of xenos (including the more massive Tyranid threat on its way) and corruption from within mean humanity will be so busy that it will never even get to try and defeat Chaos one on one.
You are spot on... The warp is an alternate dimension existing concurrently to our own... which is trippy considering that time has no meaning there. In addition the warp has its own laws (or lack there of) regarding physics and all the other rules of natural order. This is what the Chaos Gods are "born of." i.e. - The Choas gods are not built on rules...
Quite simply this fact is the greatest hurdle humanity faces in the battle against Chaos. They are not fighting by our rules. Sure we can defeat them in a battle, but the war is ultimately much more complex. Either the source of their power needs to be removed (humanity itself - not the best solution for humanity) or they need to die.
And while it is possible for a Chaos God to weaken and even die, the essences of these four are so vast that their power is virtually limitless. As you mentioned, change is constant (another tick in their column given that our dimension is built upon rules and change is one of them) so Tzeentch is not going anywhere. Things will always die, so Nurgle is also constant.
And while one could argue that anger and lust are both emotions that could be purged from humanity using technology, it is doubtful. But with all of the xenos constantly assaulting human worlds violence and pain are both pretty much constant as well and those are also aspects of Khorne and Slaanesh...
And since one of them will always exist, one will always lust for more power (wait, wouldn't that mean that Slaanesh should be the most powerful?!). And if one will always lust for more power, one will always influence humanity. This pretty much means that the only chance humanity has is with limiting their power/ influence to a controllable level.
And since the battles with all the other xenos attacks are happening concurrently to this grand battle and humanity has lost its desire for advancement, there is likely little that could be done beyond the massive war of attrition that currently exists and stalemates the demise of humanity. Nonetheless, it is all a stalemate that humanity is destined to lose due to either sheer exhaustion, fallibility, or the Tyranids.
ONE SPOILER IN THIS SECTION REGARDING ADVANCEMENT - BATTLE OF THE FANG NOVEL
I will also mention though that at this point in the game (the year 41,000) humanity is likely set up to fail despite its best intentions and even rapid changes in the status quo (like a primarch returning for example) due to what has already happened. In the novel Battle of the Fang (great book) you discover that the entire reason Magnus attacked the Fang was to stop the Space Wolves from curing the instabilities in their gene seed. He knew the attack itself was doomed to failure, but the mission was simply to destroy this potentially fate altering advancement.
The Gods of Chaos can (and already have) done something similar any time there is a serious potential threat to their survival (the birth of the primarchs and the Horus Heresy for example) - and humanity can not prepare for those interventions.
And this ties into what @MichaelBorgwardt was keying in on. Humanity needs the warp to maintain its vast empire and keep the stalemate in place. Entering the warp risks opening a door to Chaos each time. The only defense against the dangers of the warp when you are there are the Gellar Fields; but if those fail for whatever reason the window for interaction will indeed be opened. But even more, a psyker is a singular doorway for Chaos to invade, and for whatever reason more and more are born with the warp sight every day on every planet throughout the Empire - and there is no way to control that.
And until humanity can severe this link with the warp that they are born with, even if we could reduce/limit the Chaos Gods power/influence, those potential doorways being created will always give the Chaos gods a second chance to grow once more.
Emperor;s plan in a nutshell:
- Unite the humanity spread across the stars. Wipe the xenos that could enslave humans.
This has been (mostly) done during the Great Crusade - you have to remember that in many cases humans on distant worlds were enslaved by races that were worshipping Chaos Gods (You'vath and Laer are good example here).
- Starve gods by forbidding religion.
This was the wrong assumption made by Emperor - he thought, that by forbidding the worship of supernatural, the Chaos Gods will loose potential worshippers. During the crusades, demons were treated as a type of aliens and all "superstitions" were severely punished - the grand example is the Judgement of Khur where the Word Bearers were punished (and humiliated) for worshipping Emperor as god. Please note here, that he still allowed the Machine Cult to exist in peace, simply because he needed Mars and their technology.
As the @OP pointed, this wouldn't entirely work, because Chaos Gods feed on emotions as well as worship.
- Forbid the access to psyker force
By forbidding the use of Warp powers Emperor was hoping to block the small potential gaps, that would allow demons to enter the material world and spread the corruption. In practice, this order wasn't really enforced, some forces (i.e. Magnus the Red) openly kept studying the Warp.
- Allow humanity to enter the webway
Since the Fall of Eldar the webway was mostly unused. Emperor planned to open a gate on Earth, which would allow human ships to travel much safer than through the Warp, removing the need for astropaths or navigators, which (together with point #3) would in practice completely separate the access to the Warp.
This plan failed, when Magnus tried to warn Emperor about Horus betrayal - by sending the message, primarch of Thousand Sons accidentally completely destroyed the precious seals protecting freshly reclaimed webway from demons, which completely obliterated any progress Emperor made. No wonder he sent Russ to punish Magnus (and Horus twisted the orders ordering Space Wolves to kill Thousand Sons).
I think the basic idea was that once the emperor had control over all human colonies in the galaxy and established his secular society and safe human web way that he could exclude pretty much any avenue of influence that chaos could have.(master of mankind chapter 10) The warp would be so safe to traverse using his web way that nobody would encounter the corruption of it through travel, and by controlling all information regarding any sort of religion and destroying it people would have no way to access chaos through arcane rituals and the like.(Master of mankind chapter 10+11) The only way that people would encounter it might be through warp storms in real space or by encountering alien races that worship or have knowledge of chaos.(general info, only so many ways to encounter chaos) These aliens are always destroyed on contact for this reason. (Horus heresy, specifically where Horus encounters "The Empire of man" in Horus Rising, this is where the quote "I was there the day Horus Slew the Emperor" comes from. The way that corruption through direct contact with demons crusading out of warp storms is typically that regiments who fight against such horrors and are victorious have their remaining members receive an honourable execution. (Tactica Imperialis and Armageddon)
So to conclude, the emperor wanted not to destroy the chaos gods, but to remove any links they could have to humanity. Psychers he would have had to deal with also