Sure, in the same way that I don't have "pure contempt" for worms and spiders. But such a form of contempt is very rare : you can find a purpose for pretty much anything, whether you use it directly or not.
The things you reference display use in an ecosystem within which you're an active participant, whereas the Reapers stay away until action's required and return to darkspace after they're done for the next step in their agenda.
It's the second time you speak of a "chaotic burden" that shouldn't be bothered with, and frankly, I don't know where it's coming from.
The Reapers display no use for galactic life and its resources, only imposing order over their chaos and growing their numbers to aid in their dominance. Your position only makes sense if organic life serves a tactile purpose for them, and beyond reproduction and cultivation in ME2 and ME3 that's more about preserving the continuity of genetic material and paying tribute, there's never any indication whatsoever that the Reapers have any use for anything produced by the dispersal and advancement of civilizations. They're vermin, bacteria, things with which you call exterminators and pest control to take care of ... and you don't wait until they're at the apex of their glory before doing so.
You can give purpose and direction to something that's inherently chaotic (let's say trees and plants, for example) if it serves your needs, and still be contemptuous about the "tool" in itself.
You can, but it doesn't make any sense when applied to mecha-Cthulhu who are the pinnacle of evolution and the end of everything.
The idea that "contempt for chaotic life = life shouldn't be bothered with = life should be eradicated" seems pretty gratuitous to me.
There's no reason for them to stall the annihilation of organic pests they're absolutely going to annihilate, unless there's an agenda imposed that tells the annihilators to wait until some other time.
The idea that organic life is something is nothing but a nuisance "that must be killed" is nowhere to be found in what I quoted and said.
Read those quotes again, and think about words like "extinction" and "annihilation". That's the attitude being projected by the Reapers; whether it's the truth in terms of the agenda they service is something else altogether.
What reason do the Reapers have to let it grow? Well, it's easy : they use it to make more Reapers (which of course doesn't reduce the Reapers to this simple function); they elevate it and give it a better, "perfect" form (""I am the Harbinger of your perfection" ; "I am the Harbinger of your ascendance"). There might also be reasons "beyond our comprehension", but anyway, the point is that, again, the "chaotic" aspect of life isn't a problem, as long as they can control it. Going on a quest to eradicate life completely would make even less sense, especially if they're so "beyond" it.
If they're so beyond it and it's nothing but a nuisance whose extinction is "inevitable", they have zero reason to continue to let it thrive. Reapers have no need for reproduction, especially if they are so contemptuous of the material that goes into the creation of each one.
Fair enough, but other cycles were still far less dangerous and threatening for them, mainly because of the citadel signal.
If one cycle were able to do that, other cycles were able to do that, and it would be entirely avoidable by coming in sooner instead of later.
Anyway, I don't see how this argument attacks the idea that Reapers mean what they say in particular : preserve life at all cost or not, why don't the Reapers attack sooner? My interpretation is that the Reapers not only preserve genes, but also experience. They wait for civilisations to reach their apex because they can then, in the form of a Reaper, preserve exactly that : the apex of a civilisation. Don't they preserve cultures, after all?
Why would they preserve the cultures and memories of vermin, bacteria, and nuisances if it weren't in service of a higher order?