It's true that Anora is the daughter of a Teryn, but Teryn of Gwaren and Teryn of Highever aren't exactly...comparable. Not to mention that while Loghain is indeed the Hero of the Riverdane, he's still a commoner in the eyes of many nobles, whereas the Couslands have been around for centuries.
Many evoke Anora's merits, but this isn't a society based on merit alone. It's based on blood as well, along with precedent. Being married does not automatically make one part of the royal family. If Anora had a child, it might be different, but she did not. And besides, many say that Anora is capable, but I simply do not see it. Experience does not always impart wisdom.
Having Cousland put on the throne except through marriage would almost certainly have led to a war of succession, and we all know, with the Darkspawn threat, that's the last thing we'd want. The Landsmeet seems to me to be traditionalists above all. While we could manage to get unanimous support against Loghain, those still didn't count for more than that. The Cousland family wasn't friends with, or even trusted by, every other major family. Certainly not after the affair with the Howe family. Remember that, if the Warden is not a Cousland, Arl Howe succeeds, and would have gotten away with it if he hadn't been in the way.