The problem is, Skyrim would currently be mopping the floor with the Thalmor if Ulfric wasn't a head-strong idiot.
Uh... what? The Nords were fighting with the Empire, they saved the Imperial City, and the Empire rewarded them by giving the Thalmor nearly everything the slimy bastards wanted in the first place.
People who say that Skyrim can't take on the Thalmor alone are missing the point. The idea is that Skyrim should be able to rule itself, and can best organize a defense when it's free of the Concordat's yoke. If Cyrodiil wants Nord troops to defend its territory, it can ask for them as an independent nation asks another. Not demand them "or else."
This would occur if he asked Torygg to declare independence:
"Torygg, I request that we break away from the Empire, so we are free from Altmer oppression, and can worship freely."
"I respect you, Ulfric, and your motives. I think Skyrim stands the best chance united as a sovereign nation, and defeating those that would try to conquer us."
Bam, that's all he had to do. Instead, this happens:
"TORYGG! I WANNA KILL YOU! YOU WANNA DAI!?"
"I..... um.... accept your challenge?"
"FUS RO DAH! Now Skyrim no longer has a king, half the people hate me, and the other half are going to get launched into a blood civil war, in which countless hundreds will die against the Thalmor and the Empire."
No, that is not all he would have to do. He would then have to follow the orders of a feckless king who was allowing himself to be an Imperial (and hence, Thalmor) puppet, who had only given lukewarm support to independence, not enough to overrule the other jarls like Balgruuf who are hell-bent on Skyrim staying in the Empire. Torygg was an empty suit. Probably a nice guy, but useless as a king, and therefore dangerous in a time of war and unrest.