I also wanted to add that the Targaryens are especially connected with the power of Sight. After all, Daenys the Dreamer, daughter of Aenys Targaryen, is the one who foresaw the Doom 13 years before it destroyed Valyria. Only her father and family believed her, so he moved them all and their dragons to the island of Dragonstone. This is why the Targaryens survived when the other Dragon lords had not.
It’s no coincidence that the Targaryens were touched by madness, not only because of incest, but because some of them had real Visions that guided their actions. Rhaegar was driven by visions, and while it is unclear how much truth he gleaned for them and how much such visions guided his actions, he believed he was a part of fulfilling the prophecy of the Prince that Was Promised. If one looked at his actions from the outside, annulling a marriage with a wife from Dorne who helped keep Dorne under the control of the Throne, and marrying a woman who was promised to another ally of a Noble House, he looks mad. But if he had visions that made him believe that it was important to have a child who’s blood would be the blood of both the Children of the Forest (from the Starks) and the blood of the Dragon (from the Targaryens), then it’s not madness. Even if it led to a rebellion, he would have seen that there was a more important war, and he probably saw that his son, with all the magical blood he had, would be important in fighting that war. He had probably also seen the dragons reborn into the world to fight that darkness, which is why he spoke of a dragon that had three heads.
It is also no coincidence that the Three Eyed Raven before Bran was a Targaryen. Sight is a magical power gifted to both the Targaryens and the descendants of the Children of the Forest, the Starks and the Reeds, and the lesser houses in the North, all who have been interbreeding for centuries.
The world is turning back toward magic and magical blood is key to that.
