Just because he isn't an untrustworthy degenerate like most of his class does not mean he is morally "rigid" and certainly not deserving the negative connotations you apply with such terms. Ned's tragic flaw is his moral flexibility and putting love of his wife and friends ahead of his moral obligations and duties. Ned dislikes some people, but they are universally assholes. He is, on the other hand, extremely tolerant of the "victimless" crimes of immoral and degenerate nature that he encounters throughout the books. He never utters a word of direct criticism about Robert's vices, he lets his men indulge themselves in a brothel while he visits Barra & her mother, and much of the disapproval he evinces while at court have to do with their imprudence or variance from his personal tastes and not moral disapproval. He thinks tournaments are a waste of time (though allows his daughters to watch and his captain to participate) and in this case, resources the kingdom cannot spare, not a moral failure. Does he ever express solidarity with Stannis's alleged desire to outlaw prostitution? His disdain for Varys and Grand Maester Pycelle have more to do with their despicable characters and general untrustworthiness than any moral standards (unless basic decency and law-abiding behavior is what you mean by moral rigidity). His refusal to cooperate with Cersei or with Petyr's suggestion to use her children to secure his own power are not examples of being morally rigid, except in a good way - that IS treason, no matter how practical anyone with a self-serving motivation might claim it to be. Ned was simply RIGHT and in NO case EVER suffers from an excess of moral judgment. His downfall and failures do come about because he rigidly adhered to a strict code of moral behavior, but because he deviated too often, allowed his affections and weaknesses to cloud his judgment and failed in his duty as a friend, as a vassal and as Hand of the King.