If we're talking faction politics, then surely any Stormcloak success in creating an independent Skyrim would only create a new nation with a war on two borders, one against the empire and another against the Thalmor. The new nation Skyrim would also have inner turmoil because many Skyrimmers (ho-ho) support the empire and these people would have to be fought/defeated by Stormcloaks which really makes them even more assholy. Plus, the empire would also be weakened against the Thalmor and their scheme to put the whole continent under their rule.
Add to that the funny fact that the God they think so highly of actually founded the empire and it should be clear to anyone that siding with the Stormcloaks for religious/political reasons is not sound reasoning
