Bran Stark has seen what happens when men and women play Game of Thrones. Even before his ascension, he knew the human cost of war. He knew the price paid by the common people because the lords and ladies decide to take up arms to enlarge properties or swell purses. He’s a real Stark; it bears no trace of the Valyrian madness that brought down Daenerys (Emilia Clarke) and the rest of House Targaryen. He is confined to a wheelchair, so he has never taken up arms and fought on the battlefield. He spent two seasons as far away from the feud politics of Westeros as possible, and to put it bluntly, he rolled through the biggest pile of auroch droppings possible and came out with nothing on him. Everyone at the table, from silly Uncle Edmure (Tobias Menzies) to hopped up pirate Ser Davos (Liam Cunningham), has blood on their hands.
The best way to save lives, both innocent and less innocent, is to break the wheel. Ending the cycle of bloodshed in pursuit of power would not be possible at the hands of someone who has shed blood in pursuit of power. One look at Bran, the “broken” boy in a wheelchair, perfectly shows that he won the Game of Thrones by not playing it.
“Bran has no interest in leading”, – Sansa Stark
Sansa, unsurprisingly, provides the best motivation for Bran to take over as king. He doesn’t really seem to want the job. After Bran sheds his humanity and assumes the role of the Three-Eyed Raven, he’s a different person. Literally, he has grown beyond his mortal shell and has a new perspective.
This is both good and bad. Bad reasons mainly relate to a lack of empathy. As Meera Reed reminds him, Hodor, Summer, and Jojen all died to protect him and most of the children of the forest. Reuniting with his family should be cause for joy, but Bran generally seems uninterested in the reunion, if only because he knew they were all still alive from rummaging through time. However, it is more than that.
Bran’s disconnection from the living world is going to be the thing that will make him king. He is aware of the weight of his decisions thanks to the losses he has personally suffered. However, he’s far enough away from most people that he won’t be tempted to go back to old conflicts to settle scores. When one of his allies inevitably starts plotting against him, such as Sansa, he’ll be in a good position to stop him before he starts without holding his hand back to spare a loved one.