If Ned Stark had been a more selfish man instead of the pure honorable person he was, he would have taken the throne for himself. After he got Jaime off the throne, he could have claimed that shiit. It's pretty lopsided when you think about it. Ned lost his father, his brother, his sister because of the Targs. What did Robert lose? A girl he saw once or twice....the war started because of the Starks but the Baratheons benefited. I guess you can say Robert had the Targ blood but he didn't become king because of that, he got it from having a big ass army....did I forget to mention the Riverlands only rode for their cause because of Ned's marriage to Cat and Jon Arryn's marriage to Lysa. So basically Robert needed their help WAY more than they needed his. It's GRRM's world, so it's his rules. The Starks stay in the North etc etc....if this was real life though.....Ned would be like "the King killed my entire family, this is MY WAR, why do YOU get to be King?"
I woulda took the throne so quick, made Benjen The Lord of Winterfell, married Robb Stark off to Margery Tyrell to get that Tyrell bread
and guns
and allowed Jaime to quit the Kingsguard in return for Tywin not to be a fukk nikka scheming
I guarantee Ned would have been a far better king than Robert
and all of Westeros would have been better off...