Ulfric wouldn't nearly have enough manpower or any influence to face the dominion by "skyrim" alone, especially when he would still be seen as a traitor by many since his claim to being high-king is far from strong.
Ulfric also happens to be arrogant, extremely racist and narrowminded AND betrayed the monks at high hrothgar (sp).
When you first visit the palace where he speaks to his bodyguard it essentially embodies most followers of him who only see the short term future. Ulfric bases his claim on the previous king being "weak" and the worship of Talos being banned. The worship of Talos is essentially banned due to the lost war and since Talos was the founder of the septim line, it's fairly safe to assume that worship of Talos would be reinstated by Empire following a victorious engagement with the dominion.
Also I just got to a point in one mission where ulfric is basically confirmed by thalmor themselves to not be an agent of theirs, so yeah I withdraw that statement.
It's still pretty damn obvious that splitting the rest of tamriel into fractured factions and leaders would do nothing but be a boon to the dominion in the long run.