Ulfric has no authority to declare independence from the Empire.
What authority did The Founding Fathers have to declare Independence from England? By your standards...none. And you would have plenty of people who agreed with you including one of the most respected and most famous Generals of the time--General Benedict Arnold.
But it was done.
He's just a Jarl of a Hold, and he not only lacks any authority by Nord tradition or the laws of Skyrim,
That contradicts the Lore...and Sybyll Stentor...and everything we know about the social/civil set-up in Skyrim. Having challenged and defeated Torygg, he is the rightful High King (unless someone will challenge and defeat him). This kind of thing went on all the time in 10th century Gotaland (Sweden). If he doesn't have the authority to declare independence, no one does. Which is fine with the Imperial apologists but not so fine with everyone else...in and out of the game.
Beyond that, in a way that no other character in the game relevant to Skyrim, has exhibited, Ulfric represents a legitimate authority in Skyrim--one that cares intensely about the people and their culture and their Traditions and is not beholden to a foreign power.
The fact of the matter is that no historical analogy holds precisely but many give us insights into the way people behave and what has gone before. And I'm including the Lore.