Though the council chose Viserys I Targaryen over Rhaenys for the Iron Throne, he is proving to be a disappointing king in House of the Dragon, but his dynasty had several remarkably wise rulers. Indeed, the Targaryens were imperfect, but they also provided some of the best kings the Seven Kingdoms ever saw.
Still, their dynasty didn't last forever, and Game of Thrones featured a large parade of pretenders to the throne. None actually won it, but a few came dangerously close. And while some were savvy enough to make good kings, others were utter disappointment that would've surely sunk Westeros further into misery and war.
Joffrey Baratheon
Aside from being one of the most hated characters in Game of Thrones history, Joffrey is also the most stupid of the non-Targaryen kings. He is immature, reckless, cruel, ignorant, petulant, impatient, and self-deluded, believing himself superior just because he has a crown on his head.
Tyrion describes him as a mad dog, and the comparison sticks. Joffrey had zero aptitudes to rule, favoring small and petty acts of torture against those who surrounded him. He paid no mind to the everyday tasks of ruling the kingdom, meaning no one but his mother missed him when he died during his wedding feast.
Tommen Baratheon
Joffrey's brother, Tommen, was kind and well-meaning but inexperienced and easy to manipulate. Tommen's age was an issue, but he could've been a good ruler with the right leadership. If Tywin had not died, perhaps Tommen would've lived to be a fairly successful ruler.
Tommen's main flaw was his trusting attitude, making him oblivious to his ally's intentions. Others discarded him and saw him as a pawn, a figurehead they could toy with and handle to their convenience. Tommen was one of the most wholesome characters in Game of Thrones, and it's a shame his life ended so soon. However, he was never a great politician.
Balon Greyjoy
The King of the Iron Islands was the definition of a pretender. Balon rose in rebellion once before the show's events before getting crushed by Robert Baratheon's forces. His desire to be king rested on his wish to take the Iron Islands back to their glory days of pillaging and raiding, which already speaks ill of him.
Balon bit more than he could chew. The Ironborn are not soldiers; they're raiders and rapists who can fight but have no discipline. Balon's reluctance to associate with anyone outside the Iron Islands meant he had no political allies or connections, and a man who is alone can never win the game of thrones.
Robert Baratheon
Robert Baratheon was a warrior, not a king. He won the throne by swinging a hammer harder than his opponent and disliked every year he had to sit on the Iron Throne. His rebellion was to get revenge on Rhaegar and get Lyanna back, not to secure the Iron Throne.
If Robert lasted so long in power, it's because of Jon Arryn, one of the most powerful Hands of the King in Westerosi history. Once Jon died, Robert's days on the Iron Throne were counted. The truth is he had no interest in being king, so he didn't even try, instead choosing to spend his days drinking, jousting, and, in his own words, "wh*ring."
Bran Stark
As one of the most powerful magic users in Game of Thrones, Bran is a character worthy of respect. He was crucial in the fight against the Night King and will probably be a capable ruler of the Seven Kingdoms, with his omniscience giving him a considerable advantage over his predecessors.
However, Bran is not exactly human. He won't inspire devotion from the Lords of Westeros, and his lack of humanity will make him uncaring to the struggles of the smallfolk. Bran's inability to feel anything will make him cold and calculating, meaning it will again be the Small Council's task to do most of the ruling.
Robb Stark
Robb Stark was one of Game of Thrones' most interesting characters. He wasn't nearly as honorable as his father or half-brother and was willing to adopt a more ruthless approach, especially in matters of war. Robb would've been a decisive and effective king, supported by a capable council of his choosing.
However, Robb was also somewhat mercurial and easy to back down on his word. He was also short-sighted politically, unaware of how his decisions would impact him in the long term. Robb was, perhaps, the most politically savvy member of his family at first but wasn't perfect and had a lot to learn. Unfortunately, breaking a single promise to a potential ally in the name of love was not only a political miscalculation, but it cost him everything.
Cersei Lannister
Arguably the greatest villain in Westeros, Cersei Lannister was among the most complex characters in Game of Thrones. She was selfish, cruel, short-sighted, ruthless, resourceful, and absolutely unpredictable. Cersei was dangerous, willing to burn entire cities if it meant protecting those she loved most.
Cersei was Tywin's student, and while she wasn't as intelligent or effective as him, she was a worthy successor of his name. As queen of the Seven Kingdoms, Cersei shows remarkable restraint when dealing with her enemies and skill when treating her allies. She avoids rash choices in favor of a careful yet decisive approach that allows her to become a genuine threat to a woman with three armies and three dragons.
Renly Baratheon
Many people discount Renly Baratheon as a genuine threat during the War of the Five Kings. For starters, his claim is dubious at best; secondly, he dies before the war begins properly, meaning his intervention can be easy to forget.
However, Renly would've been a decent and potentially great king. He had people skills and could charm everyone through humor and wit. Renly had one of the biggest armies in Westeros backing him, a respectable name behind him, and the love of the smallfolk to boot. He was a shrewd politician who had everything to be an exceptional king - only to have crossed the wrong red priestess.
Stannis Baratheon
Stannis was stoic and self-righteous, but he was just and honorable. He fulfilled his duty to the best of his abilities, always trying to be the best possible soldier and Lord he could be. As king, he would've undoubtedly kept this way of thinking and acting.
Still, he was far from perfect. His fanatics led him to make severe mistakes that earned him the scorn of his bannermen. Stannis' overly serious behavior also left him without any powerful allies; even the Storm Land's Lords chose to back Renly instead. Even so, Stannis was clever and wise enough to accept the help of others, even if he was too proud to welcome it.
Sansa Stark
In many ways, Sansa was the perfect student, learning from Cersei Lannister and Petyr Baelish, two of the game's most ruthless players. However, unlike her teachers, Sansa wasn't cruel, uncaring, or insecure. On the contrary, her life experiences made her resilient and confident, capable of standing up to everyone.
Sansa grew up to be astute and strong-willed. Her devotion to her people was reciprocal, and her fight for the North's independence ensured the undying loyalty of her bannermen. Sansa learned the values of planning and anticipating, meaning she would always be prepared for any threat. She was a slow learner, but she learned.