Sheer attrition implies there's a constant conflict- which there need not be. Certainly there's no need for the Awakened to raid for Broodmothers against other Darkspawn- they can simply use conversion of the already existing darkspawns. Once the darkspawn hoard is under the control of the Awaken, then attrition will only occur if there's conflict between the two- which is what a separation/non-aggression pact would help with. Certainly there wouldn't be a need for a particular faction to raid for Warden blood if we had a voluntary arrangement- which itself would be a means to leverage influence and play off those factions against eachother.
No. It means a darkspawn tripped and broke its neck. People die, IRL, from all sorts of accidents. Even if we had 0 intraspecies conflict, and even if we were all ageless, we would still be extinct without reproducing because our numbers would be thinned by sheer chance injuries.
Darkspawn will die through the mere passage of time because life is dangerous. This is where the need for the rape and mutation of non-darskpawn women comes from - the inevitability that the mere passage of time will lead to darkspawn death.
Integration =/= co-existence. I'd agree on the former, not the later- after all, separate but surviving has been occuring for nearly a millenium between the surface and the deep roads.
I'm not talking about integration here. I'm talking about mere proximity. Non-darkspawn can't exist in the presence of darkspawn. Sufficient numbers of darkspawn on the surface actively eradicate life. Not just in terms of a virulent plague that poisons the land - we're talking blotted out sun, darkened skies, etc. Non-darkspawn can only exist at the whim of darkspawn. Right now, there's a detente because the darkspawn are bestial and underground. But that could change easily. It needn't be Awakened darkspawn that cause this change, of course.
There's no analogy we can have to IRL human politics or relations because we're not actively poisonous to one another. Ignoring the fact that we can resolve cultural differences from mere intermingling, we have the basic fact that we can exist around each other physically for extended periods of time.
Moreover, there's a particular question of whether the the (Awakened) Darkspawn want to reproduce. Certainly we haven't seen any indication that they've been farming broodmothers.
You mean, apart from the Mother, which has a multiple broodmothers breeding an army of darkspawn? But this is a point against the Architect. If we suddenly entertain the idea that the rest of the Awakened might be okay with extinction by way of attrition, we know for a fact the Architect is against it, because the Architect wants to preserve the darkspawn.
If the Awakened might not want to reproduce, then this is an even greater reason to immediately exterminate the Architect - because he, at least, views the darkspawn as a people that he wants to preserve in the future.
Of course there's cooperation to be had. Not only in understanding the nature of the Blight, and the Song, but in addressing the non-awakened Darkspawn, and other Awakened factions that might arise. Then there's the quid-pro-quo aspect- of providing Warden Blood in exchange for desired actions.
That doesn't work, because we're back to the impossibility of co-existence. A fundamental feature of cooperation is the hypothetical possibility that there is a possible future state that won't lead to a genocidal war of extinction. There's no such option with the darkspawn, apart from idealistic fantasies that are totally disconnected from their nature (i.e., they would voluntarily choose underground exile and isolation, and accept extinction by attribution).
More to the point, there's no evidence that there's a quid pro quo to be had, whether regarding knowledge or the equivalent of military intelligence . The Architect certainly doesn't at all suggest that there's any negotiation to be had regarding the nature of the Blight. Ignoring his methods and the methods of his crew, his sole overture is for you to clean up the mess he created.
Apart from that, we do not meet any faction of Awakened willing to negotiate or engage with anything other than violence. There's one isolated non-hostile darkspawn we meet: the Messenger. Even the Architect is hostile. Judging the Awakened darkspawn by the conduct of the Messenger is a bit like judging humans by the character of cannibalistic rapists, in terms of outliers outside the moral norm.
The rise of Awakened factions is actually one of the more compelling reasons to maintain relations with the Architect, especially if we accept that conflict is inevitable. Diplomatic intelligence- just knowing what factions there are and what their intetions are- would be invaluable. It would allow not only the tracking of the Awakened evolution, but the rise of factions more actively or directly hostile to the surface- such as the return of another 'Mother' faction, or one that wants to hunt out and awaken the next Old God, and so on.
Except for the fact that the Architect doesn't want to stop the Mother because it's dangerous to the surface. He wants to stop the Mother because she's dangerous to him and to his plans. The Architect doesn't offer darkspawn intelligence - which is to say information. He is actively hostile to you - his faction attacks and massacres the GWs, he personally kidnaps and experiments on you, etc. On our second meeting, he straight up tries to murder you with dragons!
If the Architect didn't exist, there wouldn't be a Mother. In fact, there wouldn't have been a Fourth Blight. The Mother, ultimately, was defeat in the same way an AD and a blight would be defeated: cutting off the head of the beast and having the horde flee underground. Between the choice of the Architect or the Mother, the game establishes that the Mother is far, far, far less dangerous.
The most "benevolent" Awakened faction is an active threat to all non-darkspawn life and openly hostile to it. Apart from a half-hearted apology from the Architect after kidnapping, experimenting on and attempting to kill you, we never really meet a "faction" that is anything but actively hostile to non-darkspawn, and that includes the Architect.
If the conflict with the Awakened is inevitable, knowing the factions in play will be vital. Thedas hasn't, and most likely couldn't, destroy the Darkspawn when they were stupid and hiding between Blights. The only realistic way to survive indefinitely, let alone win, will be to exploit and play of Darkspawn internal divisions. You can't do that if you don't engage.
It's pure fantasy that the any Awakened faction will actually give this information away essential to their mass genocide, which is the only information that would be of any assistance. Certainly the Architect gives you no such information - he actively lies about his own faction and motives. The darkspawn are - as far as we know - entirely unstoppable. If there's anything that the Blights reveal is that conventional victory against the darkspawn is an impossible fantasy.
Hoping that the darkspawn would cooperate towards finding the secret of a mass and absolute genocide of their entire race is silly, and everything we see about the Architect is that he's worse than all of the Awakened, because he's smarter, more powerful, and more inventive. There's nothing to engage with here. Plan A for the Architect is to turn every darkspawn into an Awakened, and it has the means to do it. That's apocalyptic. Any possible alternative is better than this one outcome.
There's just an existential threat - the darkspawn - a bigger existential threat - the Awakened darkspawn - and an even bigger and more absurd existential threat - the Architect. There's nothing to engage with here. It's the equivalent of trying to meet Corypehus halfway.