I've asked myself this question a lot as a fan of the Imperium in general.
And what I came to was: if I'm going to be getting manipulated by some entity, I'd rather have it be by a human-constructed entity like the Imperium, than weird daemonic shit from the warp. Sure, Chaos may let you break the glass ceiling through merit (although it will cost you your soul and eventually your humanity), and you have to deal with some really unpleasant looking mechanical traditions in the Imperium (to the untrained eye, half of old school Imperial art can be indistinguishable from Chaos art.) But at least in the Imperium your everyday (in the majority of the Imperium anyways) doesn't consist of one of more of the following: oceans of blood and dead bodies, large amounts of other bodily fluids produced in disturbing ways, diseases, pus, contagion or rampant, minute-to-minute mutation. I was going to add spikes but let's be honest, the Imperium digs spikes too.
In my eyes letting Chaos win would essentially give in to becoming slaves to the emotions and behaviors that underpin the big four, blotting out many other aspects of humanity. By willingly embracing Chaos, you allow them to thrive without having to do anything really. And while the Imperium is basically the antithesis of free will itself, I still find the notion of giving into Chaos somehow more repugnant. Some portion of being human means we need order and stability. Which is why I'll take the Imperium and a whole heap of human suffering and well-meaning rebellion over radically altering the human experience, and, you know, the whole universe. There's also the fact that the weak can survive and even thrive in reality. Human emotions managed by our intellects can create a prosperous environment where people can survive and be happy (or at least not in constant pain/terror/dissolution.) The Warp won't guarantee that on any level. The Warp plays to the strong, not the weak. The weak get devoured or drown in all the turbulence. Despite the wars and the exploitation, humanity does still manage to thrive in ways and places under the Imperium. To a higher degree than I think you'd find in the Warp. You might end with colonies or planets of....things. But it'd be a savage life regardless. The Warp doesn't do security and stability.
Really, if your sticking point is justice, the Imperium doesn't have a leg to stand on. Neither does Chaos but at least it's honest about its intentions. It doesn't have to lie to you (much) about your relationship. The Imperium does, so you can get through your day. If the injustice the Imperium commits on pretty much a second-to-second basis is your primary motivator, you're either going to join Chaos out of anger or eat a gun in hopelessness because neither side is truly just nor sane when taken as a whole.
And, as a Space Marine player...there is a noble, if fatalistic, sentiment to fighting for the Imperium. You're virtually alone in a world of shit filled with Chaos, hostile aliens, Space Nazism, corruption of mind and body, fear, apathy, ignorance....to struggle for the right reasons in such a place is to be truly heroic. When everything suggests you should probably just kill yourself as the most efficient way to spend your life, you offer it up to in service to others instead. It's martydom for the right reasons of the highest order. Compared to everything else in 40k, that's not a bad way to die.
All that aside, I have wondered what life in 40k would be like without the Imperium, and the often spoken assumption that it's all that stands between Chaos and its total victory. I imagine the universe would go on for a while as it was, the Eye would spread, and while Chaos would have its heyday, it wouldn't be like the total apocalyptic conversion of reality. I don't really think even the Emperor is the only thing that's keeping the eye from opening wider. I think its more relative to Chaos' sway in the galaxy. The Imperium just folding overnight wouldn't cause the Eye to tear open. What Chaos really needs is the full conversion of humanity to the cause. And that just can't happen except in the furthest flung epic fluff wankery. Humanity would resist and it would be a gradual change. For Chaos to just completely consume the galaxy, I'm pretty sure every living being with a connection to the Warp would have to become a hood-wearing, body-piercing, cult-havin' member of the religion.