It seems to me that many readers take the cosmos in cosmopolitics to be basically equivalent to the everyday meaning of that word; they take it to mean cosmos in the sense of Carl Sagan's Cosmos -- that is, as, more or less, a synonym for the universe. The only possible contrary to 'cosmos' in this sense would be 'non-existence, nothingness.'
Taken this way, cosmopolitics must either mean that politics is a transcendent metaphysical model for existence (i.e. Graham Harman's reading of Bruno Latour's Irreductions); or, cosmopolitics must mean that the entirety of existence must now be subsumed within political contestation (taking the old cliché 'everything is political' to ever more absurd heights). Neither of these interpretations are, in my opinion, especially useful (or even comprehensible).
It'd be helpful to think of 'cosmos' in broader terms. Here's what the etymology dictionary has to say about 'cosmos':
c.1200 (but not popular until 1848, as a translation of Humboldt's Kosmos), from Latinized form of Greek kosmos "order, good order, orderly arrangement," a word with several main senses rooted in those notions: The verb kosmein meant generally "to dispose, prepare," but especially "to order and arrange (troops for battle), to set (an army) in array;" also "to establish (a government or regime);" "to deck, adorn, equip, dress" (especially of women). Thus kosmos had an important secondary sense of "ornaments of a woman's dress, decoration" (compare kosmokomes "dressing the hair") as well as "the universe, the world."
Pythagoras is said to have been the first to apply this word to "the universe," perhaps originally meaning "the starry firmament," but later it was extended to the whole physical world, including the earth. For specific reference to "the world of people," the classical phrase was he oikoumene (ge) "the inhabited (earth)." Septuagint uses both kosmos and oikoumene. Kosmos also was used in Christian religious writing with a sense of "worldly life, this world (as opposed to the afterlife)," but the more frequent word for this was aion, literally "lifetime, age."For the Stoics, kosmos meant that existence was divinely ordered; it meant that, to ape Leibniz, we lived in the best and most rational of all possible worlds and for this we owed thanks to God or Nature in all their divinity. It is related to this sense of kosmos as a divinely ordered existence that we get cosmos as simply a synonym for astronomical existence generally (perhaps beginning with Pythagoras). However, the etymology of the term is demonstrably more complex and interesting than that.
So, we should take note that when Latour uses 'cosmopolitics' in Pandora's Hope, Politics of Nature and later texts he opposes it not to non-existence but to 'kakosmos' (kakos in many contemporary European languages meaning shit and in the Ancient Greek meaning bad or evil). Cosmos is, in this usage, not just a straightforward synonym for existence; it is, like for the Stoics and the other Greeks described in the quotation above, a word meaning a specific kind of ordering, a good, beautiful, agreeable ordering. In this usage there may well be no cosmos! The mere fact that there is existence proves nothing.
Cosmopolitics, in this sense, therefore means not that politics is a transcendent metaphysical principle such that all existence is political in and of itself, nor that the entirety of the cosmos must be brought within previously human-exceptional politics (whatever that would mean). Cosmopolitics is instead the recognition that since both God and Nature are dead then there is only one possible route towards a cosmos and away from a kakosmos: through politics, with all the messiness, compromise and frustration that this word entails.
It is not that the universe is always already political in itself, as though politics were some kind of transcendent metaphysical condition. It is precisely the opposite of that: there is no transcendent metaphysical condition, that's why there must be cosmopolitics.