Realistically, the Imperials would want to appoint their Dragonborn champion as the High King, as he would be an incredibly intimidating symbol of the Empire's power. And once the player has an immense reputation, the people of Skyrim shouldn't be too upset with the decision.
It just seems a bit unfortunate that the Dragonborn is so willing to be everyone's tool, soldier, savior and sellsword without demanding anything more than menial gold and equipment in return. Don't you think Tullius would have given the Dragonborn just about anything he wanted to kill Ulfric?
While I'm torn on the whole "Skyrim lets you have so many titles that they quickly become irrelevant and worthless," I figure that the same guy who is Harbinger, Arch Mage, Master Thief, Listener, Champion of the Empire, and the Dragonborn savior of the world might as well be given a title that only he is truly qualified for.
Unless he's an Elf or Beast race because... well... racism.
