Or he used the shout to demonstrate divine influence, which the empire (and the previous high-king) seem to have forgotten. Is not the power of the divine gift a symbol that Skyrim need not bow to the Aldmeri nor the empire?

That's all I can say though because I haven't even met Ulfric yet. I know, I'm despicable. I've played around 150 hours since 11.11.11. The main quest, guild lines, as well as civil war questlines remain untouched, and I haven't been to Windhelm, Winterhold or Dawnstar yet, either. I need to hurry and play through the big stories so I can engage in all these discussions a little more meaningfully.
Since I don't want to go too much into spoilers, it may be difficult for me to go into certain details. Therefore, I think it may be best if I were to approach the fundamental situation in a different context. Also, I accidentally mixed up who initially gave the power of the voice to mortals. It was the goddess Kynareth, not Akatosh.
Wisdom, and through it magic, is often considered the domain of Julianos. Magic can be seen as an extension of the divine. When one's desires are tempered with caution while gaining insights from Julianos, great acts can be achieved, which are revered by all. And yet, when these desires are not bound to anything that would restrain a person from doing harm, it can and will lead to ruin for the person acting on such impulses. An extreme example of this can be seen in the main quest line for College of Winterhold.
The power of the voice can be looked upon in much of the same light for Kynareth as magic is for Julianos. My personal impressions on the power of the voice seem to indicate that there is a much closer divine link between the voice and Kynareth than exists between the knowledge to attain magical understanding and Julianos.
My fear is that, with how and when Ulfric chose to use the power of the voice, this may, to some degree, have corrupted him, turning him away from a divine path. Naturally, I do not assume that the degree to which Ulfric may have been tainted by his own actions is anywhere near what is encountered in the Winterhold quest line. However, I do believe that the amount is sufficient to warrant a reasonable amount of concern.