I like to think Ulfric's might makes right approach would lose him support when it came time for the moot, most of the Jarl's probably only supported Ulfric out of fear he would turn on them next. None of them had any protection against someone trained to use the Voice, willing to use it against his own people to get what he wanted. The choice was theirs who would be king next, Ulric had just killed their previous choice, would they really have chosen Ulfric? Seemed to me the challenge had proved who was the better man and it was not the one who survived. Ulfric's killing of the king did not seem that honorable to me, since he chose to use his ability to shout. Elisif was too weak and indecisive to remain queen, so I doubt the Jarl's would vote for her. Throw the Empire out, let Ulric do all the hard work, then the Thalmor, the Empire or more likely his own people could do away with him in some underhanded way, and the moot would have probably chosen Balgruuf, who was a warrior, a fit ruler and honored the old ways, unlike Ulfric.
Skyrim alone could never win the war against the Thalmor, so in the end some little civil war where the Nord's fought each other probably made no difference, no matter who became Skyrim's next ruler, or who won the civil war. It was hardly the first time the Nords were at war with each other, only this time there was the Thalmor waiting to take advantage.