In a way, he’s just waiting to die. Stories about killing fill the space around drinking, eating, and wenching. His family is unimportant, the realm is uninteresting. His loss of Lyanna took a lot of caring out of him. It’s ironic that she loved someone else (as we learn later) while he pines. If she hadn’t died, he may have learned the truth about her and moved on.
And his character doesn’t arc. We, the plot watchers, are also waiting for him to die. Motivations swirl about, on hold until he steps out of the way. Credit to Mark Addy for making a placeholder interesting.
What does Robert Baratheon want? What motivation is Addy playing? “I want to die” isn’t right. He’s not even marvelously tragic. The more I think about it, the angrier I get. This is no way to treat a character.
This Robert is a Seven. Life is dull and he doesn’t care. Without luster, without fire and challenge, a Seven will wither. Only the hedonism is left.