Actually I think of Martin as the anti-Tolkien - everything that is good and noble in Tolkien (and other High Fantasy books) is deliberately left out. Every character is deeply flawed, there is no good vs evil because everyone is evil, there is no romance, only tawdry sex. He can feel free to kill off anyone because there are no heroes. It's likely because Martin is a flaming leftist and thus only has evil in his heart. And yet the books are very good, though the last was less good - Martin is falling into the "stretch out the story to make an extra buck" trap that Robert Jordan also fell in. Martin is getting on in years - hope he doesn't die before he finishes the series llke Jordan did (though in Jordan's case it was finished by a technically better writer so it worked out fine).
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.
I would consider Ned Stark a heroic character, or the potential to be. Aside from her being unable to love Jon Catlyn didn’t seem to be evil either. Also Tyrion has developed into a character I’m rooting for.