So what makes an old god an archdemon anyways? Is it just a name? If they're not associated with demons, then they're just powerful darkspawn.
Just a thought.
I hear your point though. Not sure how they survived, if BM is as dangerous as it's usually presented. It doesn't help that Tevinter seemed highly competitive as well (and still seems to be that way now). Forget demons. Social darwinism isn't exactly good longterm either.
Archdemon: I don't know of any reference that says where the name came from but almost everything "the world of Thedas" knows about the darkspawn is from the Chantry position. They oppose magic. What is the bad thing about magic that they are always warning about other than mages ruling things? Demons and other not quite friendly spirits. They believe that the darkspawn came from the event where Magisters corrupted the Golden City in the fade where spirits live. The result is the corruption of the old gods into the archdemons. Why archdemons then? Because they are something evil that came from the fade, just like demons. Futhermore we don't actually know what the Old Gods were specifically, the old Tevinter "worshipped the old gods in their dragon forms". Many things in DA have taken the form of dragons, Flemmeth, the entity of Death you fight in Legacy etc, it doesn't mean that they are all actually dragons. How do we know that the Old Gods aren't actually really powerful spirits that have been trapped in dragon bodies? It has never been revealed what they actually are yet.
I personally like the theory that the Old Gods are part of the elven pantheon (The forgotten ones) that were imprisoned by Fen'Harel (which in this theory is also the Maker) along with the Creators (who are really powerful spirits). Much of what happened to spirits (trapped in the fade by the maker) and the old gods (trapped in underground prisons) align with what happened to the Creators (Trapped in their heaven) and the Forgotten Ones (trapped in the abyss). Again, we don't actually know what the heck any of the multiple god groups are, if anything. The Maker, the Old Gods, the elven gods and so on have never (and may never) been explained.
On the why has tevinter survived thing:
Well the other big empire in the game is run on a system of ritualized murder of friends and family in order to "win" political games, Thedas isn't exactly a world where effective political systems are widespread.