The guards of Solitude are mostly Nords. Even the Legionaries are mostly Nords.
If he is so Nord traditionalist, and so honorable, and so enlightened... why they tried to chase him?
If he followed the traditions, they just have to declare him High King and hail him.
But no, because HE MURDERED the King.
If you talk to Torygg in Sovngarde he tells you how he lost in fair combat against Ulfric. End of.
So, just for fun, Ulfric decides to throw to hell the Laws of his entire province (as Skyrim was fully part of the Empire) and by killing the King. Just to unleash a civil war, who just bring more suffering to his people. splits the forces, and weakens the Empire and Skyrim.
As I said before... I can see the Dominion leaders laughing with pleasure at Ulfric′s actions.
No, he didn't believe Torygg to be a fit leader of Skyrim. So he challenged him.
So, I am right, He done that just for personal ambition. He just want his war, his Kingdom founded over the dead bodyes of his enemies.
In the time Tamriel is passing by, the last thing I desire is a war maniac king.
Lets back to my Dunmeri thinking. If Ulfric win the war, not just will ne weakened, as the Empire.
He would have free road to reclaim back Solstheim, and even send raid parties to Morrowind, as we dont see from the 1st Era.

What? Ulfric has no reason to go to Solsthiem to try and get it back
You see? If Ulfric would speaked to Torygg instead of Murdering him all the civil war may be avoided, and the united province could secceded from the Empire with a single stroke.
But Ulfric ruined it.
Once again. Fair Combat. Ask Torygg, your argument is meaningless.
His actions are proof enough dont you think ? The word "diplomacy" is not even in the deepest corner of his mind, A king shoukd be wise, and he is not.
Not to mention the religious phanatism is never so good (As a Dunmer I can largely speak of that)
He has no need to try and take Solstheim
He challenged Torygg...that is speaking, the king could have refused and sided with Ulfric but instead he chose to stand with the Empire and Ulfric proved that he was not a capable leader
This.
The so called tradition moved him to accept. When you are challenged to death, what kind of talk you can have? Ulfric went just for that. Not intention to talk.
If his intentions would be talk, no need to challenge him to the death.
I see no logic in that. He just go to kill him, thats all. With or without tradition.
But you should know Torygg respected Ulfric so much, and if Ulfric just telled him to join his cause, is most probable that Torygg joined.
But no choice were given. Challenge to Death. So IT was
Once again. He didn't have to accept. He could have been dethroned and lived.
If they talked, I imagine a dialogue like this:
Ulfric : I came here to end your life. You have two choices: die honorably or try to scape
Torygg: I have no much chances, have I ? I will never run from a traitor
Ulfric: So be it....
Utter crap. Torygg lost in fair combat. He says it himself!
That statement is pointless. We are all debaging about charactes we dont know personally (and not even exist)
For the TONE of the voice actress of Elisif I can deduce she is not lying. And that I belive.
For the things that Ulfric done during the game, I think he is an ambitious nord, that dont see the big picture (throwing skyrim into a civil war for the delightful eyes of the Dominion). And so I belive.
Torygg was murdered. And So I belive.
You believe wrong. Once again. Ask Torygg.