Robert Baratheon himself won it by war. The Targaryens won it by war.
All these discussions about who’s got a better claim are adjudicated in the book as in real life by wars or assasinations.
As to wether which one has a better claim, Jon or Dany- same rules apply. Except that Jon is willing to bend the knee, Dany not so much. I really don’t get the “she deserves it, she’s a strong woman” argument. She chooses power over love, Jon chooses love over power. She chooses hiding the truth, he chooses disclosing the truth. She knows the people are more drawn to him, but no matter because, you know, she REALLY wants the throne. So Jon, if you really love me, give up the throne, bend the knee and lie for me.
And so I move on to the “mad queen argument”. I have been rewatching the series from the beginning and you can see her tendency to destroy those who cross her from season 2. She burns the magi, she locks one of her maidens with Hotharis in a vault, but we root for her because she is the underdog, and those people had it coming. But then she starts burning her enemies, always “bad guys” until the Tarlys. These were honorable men. But they would not bend the knee. She REALLY hates it when people don’t bend the knee from way back.
As the crowning moment of irony in this episode, she is quite willing to liberate King’s Landing folk by carbonizing them. Those of you who know history will remember the Vietnam era’s famous joke- we had to burn the village to save it.
She is not “going mad”, she has since season 2 been willing to torch those who will not bend the knee
