And yet, Aerion and Aegon’s brother Prince Daeron Targaryen did have dreams that came true, even if he didn’t always understand them when he had them. Meanwhile, the other royal brother, Maester Aemon, who refused the throne, didn’t have such dreams until he was on his deathbed.
The actions of King Maegor Targaryen, known as Maegor the Cruel, were sometimes attributed to madness, but his cruel nature might have been rooted in a traumatic brain injury, not heredity. (During a trial by combat, he took a blow to the head, collapsed and fell into a deep coma for about a month.)
Likewise, King Baelor Targaryen, known as Baelor the Blessed, fasted himself to death after he also suffered a great injury. In his case, he sustained multiple snake bites in a Dornish serpent pit until he lost consciousness. Some considered Baelor a holy man, but others thought him erratic and wondered whether it was the snakes’ venom, not his genes, that had damaged his brain.
Was Prince Rhaegel Targaryen insane because he liked to dance naked around the Red Keep, or was he simply a natural nudist? We have only secondhand recollections, so it’s impossible to know whether this man was sweet-tempered and gentle, as some said, or basically feebleminded.
Queen Helaena Targaryen certainly suffered from depression. It drove her to suicide. But she also had been forced to make an awful Sophie’s Choice between which one of her two sons had to die. All three of her children had been threatened with death if she refused to make a choice, and so she reluctantly named her youngest son — only to have the assassins kill her eldest instead. Racked with guilt, she refused to eat, bathe or even look at her youngest son. That hardly seems genetic.
King Aerys II, the Mad King, was definitely mentally unstable. But then consider the trauma he suffered as a prisoner for six months during the Defiance of Duskendale. (And it’s possible that Varys helped feed the Mad King’s paranoia with whispers of traitors and treason.)