I see Logen's father as just one of innumerable petty chieftains, before the rise of Bethod from one of these petty chieftains to king. The North didn't really have royalty before Bethod, or any real concept of hereditary. It's noteworthy who your father is, but you don't earn any greater respect for having a famous father. It's not even clear that the son of a petty chieftains, could naturally expect to be the petty chieftain at some point in the future. You earn respect purely on merit.