I think an asterisk should be added to "the best story", it's the best story * for the people. Tyrion and Jon have great stories, but they also sided with Dany up until the moment she burned King's Landing to the ground. Arya has a great story, for us, but who knows her story really? And being a well oiled killing machine might not be the story you want for a King (or, in this case, Queen). Bran as a good story of trials and tribulations without being tainted by a long lasting alliance with Dany.
Sansa has a pretty good story. It would have sense for Sansa to be queen, Bran to be Master of Secrets, etc. But I think they felt they had to give Sansa her 'independence' victory instead. Sansa also had basically no claim to the throne, but neither does Bran. (Really the only reason to make Bran king is because he already has his own chair.)
Making "who sits on the throne" the climax of the show was the stupid part though. The whole point of the series is supposed to be that the politics of the throne don't matter, defeating the white walkers is what matters.
In fact, the show would have made
so much more sense if S6 played out in the opposite order:
Season opens as Dany begins a conventional siege of KL, attempting to starve out Cersei's army. She begins to show signs of madness when the people don't immediately throw down their weapons and worship her like they did in Slaver's Bay. The siege goes on longer than expected, into episodes 2 and 3, so Dany threatens to use her dragons against the city. Rhaegal dies making a strafing run against the city's main fortifications, much like in the show. She goes further mad as her advisors start to plot against her, as Jon, Tyrion, Davos, etc know that the seige is killing more and more soldiers on both sides, and wasting resources necessary to fight the white walkers.
Dany refuses to end the siege, mounts Drogon, burninates KL and sacks the city with the Essos armies, exactly like in the show. Also exactly like the show, Jon kills her, Drogon melts the Iron Throne (because it killed his mother and brother and because even he can see it's irrelevant) and recognizes Jon as the last living Targaryen (making Jon's parentage actually matter to the story, since it really doesn't in the version we got.)
KL and the majority of southern kingdoms' food to survive the winter is now ash, since Cersei and Jaime hoarded what was left in the stocks in KL and Dany burned it. Jon (atop Drogon) and the combined armies ride north against the white walkers in a final stand at Winterfel, Jon + Ayra defeat the Night's King. The armies and nobles try to make Jon king, but Bran uses his powers (again, so they actually matter) and says
that all of this has happened before and all of this will happen again, I mean, that the white walkers were defeated before and will return once again. Greyworm and the Essos armies start to turn on Jon, for killing their queen. Not wanting any more politics, Jon refuses the throne, reforms the Night's Watch, with multiple characters (Sam, Davos) pledging to join. Sansa becomes Queen, as KL is sacked, and she moves the capital and rules from Winterfel (since this story is ultimately about the Starks) and has her own hand, Bran as master of secrets, Brienne as Queensguard, etc.
Show ends with Lord Commander Jon swearing in Tormund (who spent his whole life hating 'crows') as a knight of the watch, with Jon having Drogon (fire) and Ghost (ice) by his side.
After-credits scene is Tyrion and Bronn overseeing the reconstruction of KL, bullshitting about what to rename it. Queens' Folly? Targaryen's End?