Fundamentally, the story does not make sense if Jon Snow becomes king. The story only makes sense if Jon's parentage doesn't matter, or is a liability. If you make Jon Snow king, you're just re-affirming (by circuitous path) all the fantasy mythology that Martin has been having fun with subverting and deconstructing.
Look to the Tad Williams series, Memory Sorrow and Thorn for what this is not. It's one of the late eighties early nineties fantasy series Martin has cited as making him interested in writing in the genre (as he adored Lord of the Rings but the genre was more or less dead for thirty years, filled with Conan esque pulp or theme-less LOTR knockoffs like Terry Brooks). The Williams series plays with being a bit more cynical than LOTR, but it is still reaffirming the basic mythos of a dark lord, and an Arthur story or chosen one.
So one of the core things all along Martin has been building to has been: "what if the chosen one isn't chosen?" This has been one of the core things I've been banging my head against for nearly two decades (as I've dipped in and out of the fandom), fundamentally, in the style of story Martin is telling: R+L=J doesn't matter. What is fascinating in looking at the reaction to the final season is how incredibly devoted our society and culture is to what I call "the magical semen theory of politics and leadership." Wherein if you come from magical semen but are also raised outside the system producing that semen then ipso facto you will be the bestest politician and leader EVER! It's both Nature and Nurture! This is the story we want, down in our bones! An entitled outsider, a status quo in new cloths.
Jon actually sort of hits on that directly in the finale when he tells Tyrion if Dany was fated to go nuts, then he would have to be to, but "Our House Words are not imprinted on our bones!" or some such line he has.
And I love the idea of Snow returning to the Night's watch. The show has more or less ignored/refused to deal with the subject of Snow's vows, but basically readers have been eagerly awaiting Snow's resurrection because they think Jon Snow is the sort of person who will be thrilled to follow a loophole out of a contract/oath and will then enthusiastically go off and become the much desired Secret Semen King of Destiny(!), leading men and fucking queens and riding dragons and all the deeply troubling wish fulfillment that entails.
I've sort of been maintaining since 2011 that a resurrected Jon is going to be dragged along that path, resisting every step, that he won't want to be out of his Night's watch vows or become King in the North or any of the other things he cared about before he was killed. Undead book Jon, I've long thought, is going to be more singularly focused on the undead threat, having lost much of the boy that tried to desert the Night'sWatch when Ned Stark was murdered. After we've had two-three novels with Jon protesting extensively every new honor put on him, do we really think he's going to protest his ass on the throne. Exiled, dismissed, and manipulated back to the Night's Watch is his happy ending, his state after killing Dany is the state that Ned Stark was in, but he actually does get to go to the wall, he's not summarily executed, it's a nice little parallel mostly unnoticed because of just how fast all these plot beats progress. Fundamentally, Jon is not becoming the king of oathbreaking and loopholes and there is no political reality within the mileau of the story that would make the various factions of that continent accept him as king.
Jon, by the way, will be even more invalid as a king choice in the book, because much of the point of the (f)Aegon book storyline is to salt the earth with a fake Aegon Targaryon. After we have the next 1500 page book in which all of the south-of-the-neck storyline is dealing with a fake Aegon Targaryon and the fallout of that fakery, do you think anyone--whether small folk or nobility--is going to accept that Jon Snow is actually the REAL Aegon Targaryon? Of course they won't, Martin is making it more impossible for Jon, by making everyone hostile to the very idea of his story, so it will be more clear in the book that other than the Northern factions, he has no political coalition or capital to manipulate with his name. And with Sansa completely outmaneuvering him on that front, all he will really have is the wildlings, who aren't even at King's Landing.
In the books, the Azor Ahai scene has the prince who was promised killing his spouse/love in order to prove he is a king. Jon / Dany have long thought to be likely fufillments of that prophecy, but as Marwyn says, "prophesy will bite your cock off" and I adore the Martin twist that in fulfilling (though not consciously) the final piece of the prophecy (killing his love) Jon definitively puts the crown out of reach, rather than qualifying for it via a sociopathic murder. The mythology of the past and the faith in prophecy is deconstructed, there is no magical belief lottery that is going to come up with Jon winning if you just hit the right combination of things.
By the way, I read Snow's final scene not as his deserting to live with the wildlings, the wildlings are going home, in a peace Jon has created (but that probably can't be maintained without him at the border). The Route out of Castle Black Jon is on is the route to the Wierwood tree where men say their Night's Watch vows. I see that scene as him going to reaffirm his vows, not to escape them. Most everyone on the internet seems to think he's off to frolic.
In any event, my dearest wish for the finale was that Jon's parentage matters fuck all, that the iron throne gets melted to slag and that Arya sails off into the west ala Frodo. So I got exactly my wish on those fronts, semi-sad character appropriate endings for those two characters is what I'd been hoping for!
If there was one area I think they really dropped the ball post Hodor, it's Bran.
And that, fundamentally, is that Martin does not fucking know what to do with Bran, he doesn't know any of the details of how it all works for Bran, any of the details of Bran's connection to the night king and others, All Martin knows is that Bran becomes a bit like Merlin and becomes the king in the end.
Just before Season five started, I re-read the books, And I had the fleeting thought as I started reading chapter one (just after the prologue) how ODD it was that we start the book with Bran, that Martin has said the Bran chapter (not the prologue) sprang into his head almost fully formed, that Martin has said Bran is by far the hardest character for him to write (which is why there are so few chapters), but here we are, starting with Bran. Even though Martin rewrites everything from every perspective, he didn't. So it all hit me and I thought, "wouldn't that be a bitch if the first chapter of the series is Bran and the very very very last chapter of the series is Bran. Hah. that'd make sense" I did not really think that Bran would become king, but I was thinking Bran would somehow be elevated, as I had no feeling that he was due a bittersweet ending like Arya and Jon have always seemed fated for.
I think Bran is really a giant sucking black-hole problem in the last two seasons of the show. They have fucking no idea what he is, what he's supposed to do, what he is or isn't manipulating, what his powers are, or how he really winds up king in the end. He just has to wind up there, so they got him there. All of his fatalism and pre-destination justifications I find very creepy and foreboding, I think they leaned into that a little bit, but they also gave us very little to work with in terms of suspecting whether Bran is using the pre-destination arguments to his advantage and when it is convenient, or is passively passing on information with no care for its fatalistic implications.
And I think Martin has the same problem, but I would expect that what happens with Bran is profoundly more ominous in the books than what we get in the show--maybe the Night King was trying to save the world from King Bran?