As I’ve said before, a feudal society is a society built of oaths – oaths of fealty going up the chain from knight to lord to king, and oaths of protection going down the chain. And those oaths are not incidental or merely ceremonial – it’s how property and political power are distributed, it’s how armies and taxes are raised.
Here’s how important oaths used to be: while most people think of medieval justice in the context of trials by ordeal, ordeals were an innovation that sought to improve upon the pre-existing practice of trial by compurgation, where someone accused of something would take an oath (usually on some holy relic) that they hadn’t done it, and if they could find enough people to take an oath saying they believed the accused, they were innocent.
What I would say is that the social order is under threat if oathbreaking isn’t immediately punished by the law of man or gods, if people generally begin to believe that there are no consequences for oathbreaking. Because Westeros doesn’t have any social institutions that could function in the absence of this system, so the Hobbesian war of all against all would be coming along very fast and it would stay for a while.