I wouldn't call Elisif competent either. Not yet. But with the advisers she has, her empathy for her subjects, and a little time, I believe she could be a good ruler. In the mean time, she would have Tullius on-side to assist with military matters; it's stated by one character (can't recall who) that one of the reasons Tullius is in Solitude is to advise Elisif. I was never particularly taken by Ulfric's current advisers, who seemed more like old war buddies appointed to various posts, but YMMV.
Last point: Ulfric agrees to the Moot after replacing any Jarl who would oppose him. That's an overthrow in my books.
I think there are good reasons to support either faction. I obviously have my pick

and I'm kind of constitutionally unable to support the Romans. However, just as people say that this isn't the time for Skyrim to declare independence, I would say that this isn't the time for on the job training for a passive ruler.
Ulfric doesn't submit to the moot until he's already gotten some military victories, that's true. But if it were my PC calling the shots, Elisif would not have kept her head let alone her jarlship, and I wouldn't let Balgruuf sit around and make threats towards Ulfric, either. So Ulfric is not nearly as bloodthirsty as he could be, and as a similar ruler in actual medieval history would have been.