Except that Akatosh gives the Dovahkiin those powers to bring balance to the world, which is something specifically stated by the Greybeards. It was Dovahkiin's destiny to be born with the dragon blood and therefor be able to defeat Alduin and his fellow dragons. Heck, even the Greybeards tell you after their initiation that you should not shun your gift and use it the way Akatosh bestowed it upon the Dovahkiin. How he wants to use it is left up for debate, but the overall consensus is that the Dovahkiin is a hero and that he uses it for good, though not all the time. Besides, it is entirely stupid of you to try to assert your claim by stating opponents that are usually hostile out in the wild, and therefor forfeit that chance to have an honest fight.
Thing is though, the high king was far weaker than Ulfric, who had legion experience and Thu'um experience under his belt. The only training the high king had was probably decent swordsmen training to defend himself; however, how can you expect to defend yourself when your enemy brings an unfair advantage, thing is you cannot.
No, that is not what I am saying. I am saying that because Ulfric knew he could beat the high king without so much as a fight, he is a true coward. Only a coward preys upon the weak and young to fit their own needs.
While it is true that kings can be challanged, Ulfric's reasons were not for Skyrim, but for his own selfish agenda, which is even mentioned by some of his fellow soldiers.