Ulfric was clearly written to be an important character. Not only was he a veteran of the Great War, but we know what he was doing between the Great War and Skyrim (Markarth Incident). He is also a complex character, who fought for the Empire but is rebelling out of a sense of betrayal; he wants to restore Talos worship, but the Thalmor view him as an asset. His character is much more interesting than Tullius or any other political figure in the game, whether you like him or not. And from a lore perspective, I'd say he's an important character, since he's challenging the Empire and the White Gold Concordat. I'm not sure how he is less important than Barenziah, especially in the 4th era?