The 'nids deaden the Warp wherever their fleets are so I guess if they got big enough they'd null out the whole thing.
The nids don't cancel out the warp, what is called the "Shadow in the Warp" and accompanies the approach of the Tyranids is the presence of the Hive Mind in the Warp - each psyker that tries to tap into the warp while in the reach of the Tyranid synapse has to push past this presence and defend against its attacks, which is why the psykers on worlds under attack die or go mad
The old Necron fluff was about calming and blocking out the Warp ... but that is no longer the chase since Necrons are now more then just the mindless armies of the C'Tan (and the C'Tan are funcionally dead)
From a lore perspective, can the nids actually threaten chaos? Or could they just hide inside the warp forever?
The power of the Chaos gods is derived from the existing mortal souls - since they can tap into all the expanse of humanity, they are as powerful as they are in 41st millenium ... killing off every mortal in the physical realm would greatly deminish their strength, if not threaten their existance
The problem if the followers of Chaos were hide in the warp the mortals would be drawn into the conflicts in the Realm of Chaos, which for one only has physical attributes when it has accomodate mortals - otherwise it is just "waves" of physic energy - and secondly would lead to them all dying in a conflict since in the Daemons are not as fragile as they are in the material universe . On top of that mortals would be exposed to the effects of the warp which lead them to be possessed, mutated and/or preyed upon my daemons for power which all in the end would find kill them... Chaos is not exactly a safe life choice unless you actually make it too daemonhood (become partial to one of Big Four, functional immortallity and health benefits included, until they are sick of you and reabsorb you)
I might be in the minority here but some of the best Warhammer 40k stories I read were not very friendly with the Imperium (e.g. "Lord of Night" had a superb subplot that showed that event the authority of the Inquisition doesn't help you if you are a psyker or a mutant, an angry mob will try to lynch all the same while Arbitres are content to watch)
Given that this is the franchise which invented the term 'grimdark' I don't think you're in the minority there; but the grimdark Imperium is far more characterful and fun than any of the grimdark other factions.
Because there is more there and what is there about xenos is usually functionally only to provide antagonists which show us the attributes of the Imperials...
The intersting part about e.g. the Eldar is hidden in the margins only by the want of space - the Craftworlds are not a single monoculture, thought the Path is a dominant neccesity (Eldar who are not on the Path cannot live on the Craftwolds because they could not comprehend the way the CW Eldar organize), and are different from each other:e.g. Biel-Tan is not ruled by the Farseers like the rest but the Court of Young King (the most powerful exarchs) shares equal power, Saim-Han is less a unified society but a bunch of clans who happen to have taken the same boat out of the old Eldar Empire, Iybraesil is a matriarchy as opposed to the -implied- gender neutral societies, Iyanden's Spiritseers are no longer able to put the dead eldar of their Craftworld (given new bodies as Wraithguard) to fully rest which leads to them "living" with their living kin etc. etc.. Even their goal are different by degree: e.g. Biel-Tan and Iyanden want to reclaim space for a new eldar empire, Lugganath would rather see the Eldar flee the material universe and hide in the webway (like the Harlequins, as well as most of the Corsairs and Dark Eldar)...
I could go on but since I don't have reprint of the Doom of Mymera, which revises the Corsair-fluff, I rather not