What makes Oedipus the King of Tragedy?
It is a fairly lofty claim to argue that Oedipus is a "King" of tragedy. He has to be up there by any standard of what defines tragedy. I am not sure he is the only "king" of tragedy, but he is a king of a tragic predicament on many levels.
In my mind, the most fundamental level on which Oedipus is a "king" of tragedy is that his tragic collision is caused by a genuine sense of goodness. While he might display some bad habits in the treatment of those who disagree with him, he operates as a fundamentally "decent" human being. He seeks to find out why his subjects suffer. That is the reason for all that plagues him. In order to alleviate the burden that is placed upon their shoulders, Oedipus demands to find out the truth, as horrific and awful as that is. If Oedipus did not care about his subjects, he would have simply concealed his own past or simply discarded it in the face of their suffering. He suffers because he feels that their suffering must end. He becomes a high figure in tragic proportions because of his having to "take the hit" in order for his people to live lives of happiness.
Additionally, Oedipus has to be seen as fundamentally human. His beliefs in his own sense of superiority and hubris are uniquely human. He fails to see himself as inferior to fate and the gods. Literature has proven that this is not something that only he experiences. He is not the first nor certainly the last to believe that he can outrun his fate. For being human he suffers tragic dimensions and would represent a high level of tragic collision.
Finally, I would propose that the horrible condition of Oedipus' sin is something that would make him a valued member of the Tragic Hall of Fame. Whether it was self made or something that is simply outside the realm of his control, it's a fairly awful fate to have killed one's father, marry one's mother, and have children through her. Merely writing it is pretty horrific. The fact that his mother/ wife kills herself, and he blinds himself, dedicating himself to the betterment of his children all help to contribute to Oedipus as a definite king of tragedy. I am not sure there is much else. Even if one concedes everything was his fault, something that I am not ready to fully do, it is a high point of tragedy to see Oedipus at his lowest point at the end of the drama.