I think Ned's death is meant to signify the death of chivalry/honor. For the rest of the series, each main character makes a morally grey or outright bad choice. Martin is telling the audience that such a heroic and honorable character cannot and will not exist in this world. Such steady chivalry and honor are hard to come by in a fight for power and it doesn't survive the fight when it is found.
I love this show and I have loved analyzing it from this new perspective. The intense ties to my family really interested me this time around. Theon's obsession with his homeland, Jon wanting to leave the wall for his family, the Lannisters caring about Tyrion's death, etc. In the other Medieval stories we have read, a person's family does not feel as important. Lineage is mentioned to prove that someone is worthy or the rightful heir to a throne, but there isn't the same intense obsession/loyalty. It is regularly mentioned that Gawain is Arthur's cousin, but it is more of a fact than something that is used to aggressively bond them. I often forget that Gawain is related to him. The only time it truly seemed important was in Gawain and the Green Knight and even then it was not on the Game of Thrones level of importance. Everyone in Arthur's court seems to care more about that allegiance than that of their family. There is no talk of personal family crests and mottos. In this way, Arthur's court reminds me of the Night's Watch, once you join that is your family.