The Stormcloaks are not racist. The denizens of Windhelm are, to Argonians and Dunmer, but leave everyone else alone. Including Imperials and Altmer.
The Stormcloaks also plan to take the fight to the Dominion. How are they going to do that without leaving Skyrim?
The only way the provinces would fight together is if the Dominion attacked two provinces again. Hammerfell is just as unlikely to help the Empire, and Cyrodiil helping Hammerfell (if just HF is attacked) would break the treaty. If just Cyrodiil is attacked, Markarth's Nord population WILL die if it's under the Empire, since the Forsworn are breathing down it's neck. And the Empire wouldn't care, because Cyrodiil is more important than those filthy Nords. That's how they lost the Reach, because Imperial City > Everyone else.
This is not the Allies of WWI and II. This is an Empire. It cares about Cyrodiil. The Legion is respectable. Even Redoran thought so. Those nobles in the IC? Not so much. Do not use the Legion to judge the entire Empire.
If the Empire falls, Dominion will destroy Skyrim anyway. Dominion's ultimate goal is eliminating all of the humanity.
Will it? People seriously overestimate the Dominion. It had difficulty defeating an unsuspecting Empire. Can it really plow through Skyrim, Hammerfell, Cyrodill, High Rock, and Morrowind?