It turns out that a lot the groundwork that GRRM, Benioff, and Weiss laid with Bran's character never led anywhere.
The first chapter in Game of Thrones is from Bran’s point of view and begins like this, with a reference to summer:
|The morning had dawned clear and cold, with a crispness that hinted at the end of summer.
Bran is portrayed as a curious and sensitive kid who has not yet experienced the hardships of winter. As a lord's son, he has lived a sheltered life and never lacked any comforts.
|“Oh, my sweet summer child," Old Nan said quietly, "what do you know of fear? Fear is for the winter, my little lord, when the snows fall a hundred feet deep and the ice wind comes howling out of the north. Fear is for the long night, when the sun hides its face for years at a time, and little children are born and live and die all in darkness while the direwolves grow gaunt and hungry, and the white walkers move through the woods”.
In the beginning of Bran's story, the white walkers are little more than an old wife's tale, but even as such they carry a large threat. The last time they appeared, during the Long Night, winter lasted for generations and almost led to the collapse of human civilization. Winter and the white walkers stand for a metaphysical threat - they are destruction, obliteration, death.
When the Stark siblings get their direwolf pups, Bran is the last to name his.
|He had tried a hundred names in the last fortnight, but none of them sounded right. […]
Bran’s Summer came last. He was silver and smoke, with eyes of yellow gold that saw all there was to see.
The names of the direwolves are significant. Bran is the summer child, with the summer wolf, and there's weight in that name. Summer is the opposite of winter, and when winter stands for death and obliteration, so does summer for life and the living.
Right from the beginning of his story, Bran is situated in opposition to winter.
When Jaime pushes Bran from the window, he falls into a deep coma and his family has little hope he'll see the light of day again. But Bran is not yet gone. He dreams of falling from a great height, while a raven with three eyes urges him to fly. We later learn that the Three-Eyed Raven is an ancient, mysterious man with Greensight, who watches the past, the present, and the future. He resides beyond the Wall and tries to activate Bran’s magical abilities.
|Bran could everything so clearly that for a moment he forgot to be afraid. He could see the whole realm, and everyone in it. He saw Winterfell as the eagles see it (…) North and north and north he looked, to the curtain of light at the end of the world, and then beyond that curtain. He looked deep into the heart of winter, and then he cried out, afraid, and the heat of his tears burned on his cheeks.
Now you know, the crow whispered. Now you know why you must live.
link to the artist
Bran is the first main characters who learns that the threat of the white walkers is still very much present, but struggles to fly, to awaken his own Greensight. Magic is a dangerous force in Westeros, and the Three-Eyed Raven tells Bran he will die if he hits the ground. He wouldn't be the first person to suffer this fate.
|There was nothing below him now but snow and cold and death, a frozen wasteland where jagged blue-white spires of ice waited to embrace him. They flew up at him like spears. He saw the bones of a thousand other dreamers impaled upon their points.
This means that the Three-Eyed Raven goes to great lengths to awaken another greenseer. Why is Bran specifically so important to him? We know that he's not the only greenseer in Westeros. One thing is for sure: Bran’s story is never about the game of thrones. Right from the beginning, his story is about winter and the white walkers.
Bran’s Greensight might have been awakened, but he has difficulties truly understanding both his dreams and his warging abilities. He meets Jojen and Meera Reed. Jojen is gifted in Greensight as well and tells Bran it's of vital importance that he makes his way north.
|Bran: "What else did you see?"
Jojen: "Only one thing that matters. You."
|“I dreamed of a winged wolf bound to earth with grey stone chains,”Jojen said. “It was a green dream, so I knew it was true. A crow was trying to peck through the chains, but the stone was too hard and his beak could only chip at them.”
Jojen's dream was planted by the Three-Eyed Raven, who utilized a more susceptible greenseer after he failed to get the message across to Bran. Once again, this stresses Bran's importance (especially since the Raven could have much easier called on Jojen himself rather than activating Bran's Greensight).
The group around Bran make their way north, but the journey is hard and takes a huge toll. The all-encompassing threat that the Night King and his army of the dead pose becomes more and more evident. It also becomes clear that this enemy can't be defeated by normal measures and that Bran's journey is directly tied to the survival of humanity.
When Bran finally meets the Three-Eyed Raven, he says this:
|Raven: "You think I wanted to sit here for a thousand years, watching the world from a distance, as the roots grew through me?"
Bran: "So why did you?"
Raven: "I was waiting for you".
The Three-Eyed Raven teaches Bran to utilize his Greensight. When he dies, his consciousness merges with Bran's and effectively makes him the new Three-Eyed Raven.
The Night King has taken an obsessive interest Bran for a while now. Bran tells everyone why that is:
|Bran: “He wants to erase this world, and I am its memory.”
Sam: “That’s what death is, isn’t it? Forgetting. Being forgotten. If we forget where we’ve been and what we’ve done, we’re not men anymore. Just animals. If I wanted to erase the world, I'd start with you.”
The Night King's motivation seems a little flimsy given that Bran mostly sits in a corner and makes uncomfortable comments when you least expect to; it's not like he's about to start Wikipedia. In addition, the Night King was interested in Bran before he became the Three-Eyed Raven. But let's accept his motivation at face value.
As the white walkers descend on Winterfell, Bran offers himself as a bait and waits for the Night King in the Godswood. (Side note: shouldn't have there been an ambush lying in wait? They're lucky Arya got there in time...).
In the end it's Arya who kills the Night King. Of the main characters, she's by far the most stealthy fighter and has unparalleled skills, so it makes sense in that regard. However, we have been told for seasons that no mortal weapon can threaten the Night King, only to have him die by a single blade of dragon fire-enhanced steel (while being impervious to actual dragon fire). It's exactly what we've been told wouldn't destroy him. The Night King has been a metaphysical threat since his first introduction, but was killed by profane measures.
This ending falls flat particularly for Bran's story. It took great sacrifices to make Bran the Three-Eyed Raven, which usually leads to an equivalent pay-off, something the sacrifices were for. There was the implication that Bran would need unique abilities to help fight the white walkers. This is not what happened in the end. It didn't matter what he can DO, only what he IS.
It can be argued that Bran knew that the Night King could only be defeated in the Godswood, only in that particular moment, and that all the events (from the last thousand years) had to fall exactly into place in the way they did. But this is hardly what really happened. In the Godswood, the Night King was not much more defenseless than anywhere esle. If Arya could sneak into their midst of the assembled generals and scale a tree undetected, she could have gotten to the Night King in countless other ways too. There is no singularity to this specific moment.
Not much! In the show, Bran has been a useful plot device because he can connect disparate story lines, becoming an easy fix for all kinds of headache-inducing storytelling problems. But how much information will he want to share in the future? It's unclear if enough of his personality remains to make him invested in the fate of his family, or in politics in general. The original Three-Eyed Raven manipulated some political events in the books, but only seemed to want to put key players in position before the Long Night.
Since it's unlikely that Bran will participate in politics or in his family's life, what else is there left for him to do? He's a shell of the person he once was. Bran's superpower of moving the plot along might be used some more, but he has outlived his purpose at this point and will probably die in the remaining three episodes.
There is no saying how Bran's story could play out in the unpublished books, since the Night King hasn't appeared there and it's doubtful he ever will.
Sources: 1, the books
This is the quintessential tl;dr, but I needed to get this off my chest.
[Spoiler (click to open)]Huge spoiler.[Spoiler (click to open)] After reading the last rounds of spoilers, it's safe to say pretty much every character's story arc falls flat. Oh well. Should have seen this one coming. Joke's on us after we've invested years into this story.