It is a realist approach to fantasy, to make a sort of oxymoron. Martins people are real people, imperfect. And he has killed off some of the most upright.
Consider the Iliad. For all the gods and goddesses, magic and myths, it reads very much like a modern novel.
The best of literature is full of compelling but imperfect characters. In the Iliad the best man is killed and the most annoying man manages to eventually get over himself, at least a little.
Respectfully disagree. Martin's "reality" is what we would be like if there were no Sovereign God running the show. God calls real people to be better than that. I think Martin has done a good job depicting a Godless world - but that's not realism (except in leftist fantasies).