Hmm... Eradicating the darkspawn, you say? Well, that's been a plan of some character or other since Awakening, and actually, first mentioned in Origins. I just don't see it happening anyhow, and here are a few reasons why:
1) The Deep Roads are vast and very complex. So far, it even seems that large parts of them are still unexplored. To eradicate all darkspawn, you'd first have to explore them. A feat even Grey Wardens, even when their numbers counted in hundreds, seemed unable to do.
2) Darkspawns are a product of blight and that can exists independently of host. Even if one woudl eradicate the current generation of Darkspawn, in a few years chances are someone somewhere will get infected again. This will creat new darkspawn and it all starts anew. Even using some Qunari boompowder to seal the tunnels off, I think it will start to reek somewhere.
3) Seemingly the only option would be to drive the Darkspawn deep enough in each and every region to seal them off in a thaig and hope they will die off. However, such huge scale campaign seems impossible unless all surface nations are united, which I don't see happening in the short-term future (or long-term, unless everybody suddenly converts to Qun)
I could continue the list, but I think those three major points are sufficient for the discussion of this matter.
Furthermore, even if the Darkspawn will be eradicated, I think it won't solve almost any problems. True, it might usher Thedas into ant age of scientific and thaumaturgic prosperity - as evidenced by the fact that containing the Fifth Blight has already had effect on the world - but chances are that some will break the taboo again. Would no-one do, well, that could get interesting. But the lack of Blight has already brought two major conflicts into the world (one could say that would the Fifth Blight endanger Free Marches, the templar/mage war would likely never break out because they will sooner find a common enemy and then you have the war in Orlais which too is likely due to lack of suitable enemy for Gaspard and his men), so actually ending them once for all might plunge it into total chaos and dissaray. In conclusion, maybe it's a good thing that none of the plans have succeeded so far. 