Sorry, but "The Thalmor would magically be able to achieve the same result under all circumstances" isnt that compelling an argument to me. Ulfric already had a personal militia for like 20 years before he killed the king. The logistics for a civil war don't just happen over night.
Beyond that, even if another populist leader does emerge, theres nothing that says that he's as politically unsavvy as Ulfric. Surely "the elves want us to fight" would be a very strong idea if it were actually able to penetrate the Stormcloak psyche.