This isn't something I paid much attention to at the time, lost in the general miasma of incompetence that hung over the whole final season. But looking at the people gathered in the council room, more interested in dirty jokes than ruling....

There's, off-screen, the Maester who is being accepted as the official historian of the period, and who left one of the key players completely out of the official history. Also, they gave the job to a doctor by profession. Also, he's way too dumb to court royal patronage, and they're too indifferent to image politics to make sure the histories are being written by someone interested in staying on their good sides, if he's going to be a fabulist.

Then there is the actual administration.
Brandon, First of his Name, called the Broken, of House Stark, King on the Mobile Throne
Tyrion Lannister - Hand of the King
Ser Brienne of Tarth - Lord Commander of the Kingsguard
Grand Maester Samwell
Lord Bronn of Highgarden - Master of Coin
Lord Davos Seaworth - Master of Ships

Davos knows how to sail A ship, but he's barely literate, and his one attempt at commanding a fleet was the disastrous defeat on the Blackwater. Is a smuggler the guy you want handling the bureaucracy of a naval force and determining naval strategy? He might be the best of the bunch, too.

Bronn, just a couple of years ago, was so ignorant of finance to the degree that he didn't understand loans and borrowing money. He too, is possibly illiterate and innumerate. Also, he's thoroughly established as purely venal, motivated primarily by the acquisition of money. It's one thing to replace the guy who probably stole the treasury through accounting schemes and fake loans and investments to himself, with someone who is incapable of carrying out the same sort of fiscal shenanigans, but he's even more nakedly motivated by greed.

Sam might be smart, but there's lots of smart people in the realm. The point of the Grand Maester is to be formally educated and have the knowledge base available to give the King and Council. And Sam's a dropout. Not only that, it's one of those positions that requires a solemn oath and a dedication to service and the rules above one's own interests. That the point of maesters, that they be absolutely trustworthy, which is why they forswear family and marriage and lands and titles, because those are the loyalties and desires and ambitions that motivate powerful people in Westeros. Maesters take themselves out of the game, so you can trust them to advance your interests instead of their own. And Sam has repeatedly proven himself one of the worst people in Westeros to trust in that regard. He ignored his oath to Night's Watch to have a relationship with Gilly and help raise her kid, he decided to leave the Wall and go to Oldtown to advance himself and admitted out loud that his motivation was to protect his concubine and adopted child, neither of which a brother of the Watch is supposed to have for that exact reason. He stole a noble family's sword in order to vindicate his own self-worth and then he bailed on the Citadel once he found some information about his friend that might be useful. Yeah, he also discovered some stuff about dragonglass, but it was nothing he and Jon didn't already know. So what's going to happen the next time the best interests of Gilly and her slow-growing infant conflict with the duties of the Grand Maester or the interests of the crown, or Sam decides he can do better for himself in some other way?

Brienne might have warrior chops, but her job is actually to faithfully protect the king above all else. What happened the last time she had a job like that? She abandoned her post and left Sansa helpless in a castle with a sadistic rapist, so she could pursue a personal vendetta and murder a wounded man because he preemptively killed a guy who was planning his death, but was nice to Brienne at a party once, even if he could act civilly with his own brotherdo so hot as at a parley.

Tyrion did okay as Hand of the King...in Season 2, but ultimately, he had to be bailed out by Daddy and the Tyrells. He didn't do so hot as Master of Coin, and then he was a shit regent in Meereen and a lousy advisor to Dany. In Meereen he either let the slavers lull him into a false sense of security by their seeming acceptance of his truce, or he anticipated their treachery, which I seem to recall was implied, but did nothing to prepare for their attack, and again, had to be bailed out by the cavalry coming to the rescue. As Dany's advisor, he frittered away her enormous military advantage by scattering her forces around Westeros for Euron & Jaime to defeat in detail. The other aspect of his role was to curtail her Targaryen tendencies to madness and violence, so epic fail there. Even his approach to palace intrigue was inept, such as when Varys lost his damn mind and decided to stan for King Jon when not even Jon himself was on-board. Tyrion failed to curtail it in time to keep Varys from getting in over his head, and then didn't do anything to cover his own ass, so that when Varys was exposed by his clumsy & public acts of treachery, Tyrion looked either incompetent for failing to catch the traitor or treacherous for failing to act on what he knew. Tyrion more or less failed at everything since shooting Tywin, and even got outsmarted by both Jaime and Cersei in the penultimate season. He was only one of several voices in the chorus that impelled Jon to take out Dany, so it's hardly like he can be credited for advising Jon there. Even his metatextual ramble about stories came down to claiming Bran has the best story, when the storytellers themselves, who threw in such gratuitous nonsense as the raid on Craster's and Theon's torture scenes, didn't bother with Bran's story for a whole season.

And in adapting a story that deconstructs the fantasy idea of a king, with a strong thesis that the ultimate measure of a good king is that he protects the people, we get Bran Stark on the throne, who is detached, indifferent, and it is implied, foresaw side suffering several military defeats and the massacre of a city full of innocents and allowed them to happen, in order to clear his path to the throne! As with Sam, as with Brienne, as with Bronn, what's to say he won't do the exact same thing the next time his interests dictate?

TL;DR - Game of Thrones was not a good show.