In a round about way, this is a good thing. Our casus belli for reconquering the Seven Kingdoms is Robert's incompetence in the face of a changing world has made him unfit to rule. Not just unfit, a failure so great that he is a danger to his own people greater than even the Mad King who would have burned all of King's Landing and all of its people as final act of spite. It would unreasonable for every last Lord and Lady to swiftly take action and successfully secure protections for their people. They lack the support, and that is where we come in.
[X] Crake
Well, that by law of succession, it's not his throne, is Casus Belli enough. After that, it's no longer a question of quibbling about legitimacy. Once you fight through everyone between you and it, once you have consolidated your gains, it is a matter of who supports you, what benefits they get out of doing so, or conversely, opposing you.
The thing that Stannis spent too long doing in canon was being irate that the Lords would not heed him or swear fealty to him without some tangible benefit toward doing so, or an incentive to oppose their rivals to accompany it (they do).
Robb assumes that people will not act of their own initiative and self interest if he wastes time doing things that don't actively benefit them or acts in ways that bleed away support, supposing perhaps that he can't be beaten on the field when most who would become an enemy are perfectly happy to kill you when your back is turned or when you're least suspecting (they will).
Tywin thinks reputation is all you need to keep our grip on power, fear of retribution will keep people from trying to kill you (it doesn't).
Hoster thought that creating ties between the people who are in power
presently would secure his House's future (it didn't).
Robert thinks you can smash anything that threatens you until it doesn't any longer (he can't).
Mace thought he could wait everyone out until an opportunity presented itself to take power for his House and solve the question of who's in charge by marriage (who could? Even in canon? The Dance proved
expected succession is a shaky rock to build an empire on).
Not even going to explain Balon's thought process (simple answer: He didn't think).
Doran for example is the closest to realizing the truth that we realized, he's not perfect but for his respective position? One where no advantages exist? He understood that:
No one knows jackshit about what they are doing. That's the secret of the Game of Thrones. Everyone has
assumptions and they are all wrong.
The only reason to rule is your own. The only right you have is what right people believe you possess. There are a million ways to convince people you have that right. If enough people don't agree, then they will all act to take it from you. Making an assumption that you will win based on what you suppose should work is not the same as
knowing you will win based on the facts of the situation, knowing the motives of other people, and then attempting to convince them that your goals aren't mutually exclusive. If you do this enough times, it doesn't matter if you don't get everyone to agree that you should be in charge, they will only act when they believe they have an advantage, just as you would against them, or conversely, act to create an advantage where none exist.