I am sorry but to me family connections and the reason people do things make the series endure. George RR Martin world is so interesting for he causes you to connect to his characters, everyone is motivated to do what they do due to some personal belief system, Martin makes you understand his characters and what drives them.
Take away the people's belief system
Take away the family trees and connections, and the world of ASOIAF would be very very different. Littlefinger would not have become what he is, if Brandon (Ned Stark's deceased older brother) was not a bully to him. Roberts Rebellion would not have happened if 5 different things would have happened. Some of these looking back may seem trivial but to the character eyes at the time it occurred they are perfectly natural.
Part of me loves the hedge knight novellas because they specifically go deeper into the ASOIAF world lore.