ned being held up as the metric for moral goodness in asoiaf is absurd like did you not read bran i, agot in which he beheads a man on the run from the others because he must fulfill his fedual oaths and he carries out the execution through his family's ancestral sword which was definitely forged for the exact opposite purpose, i.e. in defense of the north against the others. and then he uses ice again to behead the direwolf which was meant to protect his daughter. is it any wonder that he also meets his end the same way, through it, after spending the rest of the book in king's landing in service to a failed king, desperately trying to reassure himself that they are not repeating history. bran i is saying ice was already metaphorically broken long before tywin melted it down because the starks have forgotten their magical history yes, but also because ned represents an older, failed generation in service to hollow chivalric ideals. and it is now up to his children, the ones coming of age in a world destroyed by the previous generations—it is up to bran, sansa, arya, and jon to reforge their family legacy, away from contradictory oaths and in service to hollow paradigms. (and in a way ice is already currently being remade through brienne, who is not a knight of the songs but still the closest thing to the idea of a true knight)