So why did they chose the characters they did for this and leave others out? And who the fuck is Rickard Stark???
Because there are a million characters as it is.
You know how we were talking about Rhaegar supposedly kidnapping Lyanna led to Roberts Rebellion? Well that was just the start of it. The Mad King BRUTALLY killing Brandon and Rickard Stark is what really set things off.
Execution
After Lyanna's abduction, her older brother Brandon was enraged and rode to King's Landing demanding the release of his sister and the death of Rhaegar. Aerys arrested him for treason and called for his father to come to the capital to ransom him. When Lord Rickard complied, Aerys, now utterly mad, arrested him for treason as well.
Lord Rickard demanded a trial by combat. Aerys declared "fire" the champion of the House Targaryen and had Lord Rickard suspended from the rafters of the throne room while pyromancers lit a blaze beneath him. As he burned, Brandon was brought into the throne room, a leather cord attached to a strangulation device was wrapped around his neck. Aerys told Brandon his father was a dead man but there was a chance to save him. A longsword was placed on the floor just out of Brandon's reach. And the more he struggled to reach it, the more the cord tightened around his throat. Brandon Stark strangled himself trying to free his father, who was roasted alive in his own armor. The entire court stood and watched this atrocity take place, Ser Jaime Lannister and the Kingsguard among them.[1]