One general attribute of feudal societies is that they respect laws or at least try to interpret them in one own favour. Succession laws are one if not the most important laws in a kingdom, not respecting them meant low legitimacy and that led to rebellion.  Blood right was so important to Westerosi society that Robert was to be king just because he was the closer to the succesion after the targaryens. Robert took the throne because he had the army, the claim (being that the current dynasty