Another reason the Stormcloaks shouldn't be allowed to come to REAL power in Skyrim is a matter of Economics. First off let's focus on Whiterun Hold, specifically the City of Whiterun, home to everyone's favorite Jarl (maybe) Jarl Balgruf the Greater. Whiterun Hold and the City specifically, are where the majority of Skyrim's trade with Cyrodiil comes in should the Stormcloaks control such a pivitol point trade with Cyrodiil would cease therefore hurting the local economy and the economy of Skyrim as a whole. A well known fact is Nations run on Currency something like that would severly cripple Skyrim's.
Another well known fact is that the East Empire company (after re-opeing) creates alot of work and productivity and cash flow for Skyrim and being an Empire funded company it can easily be removed from Skyrim by a snap of the Emporer's finger. Do you really wish to damage Skyrim's economy and force the people into a poverty and sickness stricken life all for the sake of Talos Worship? A noble cause it may be, but highly un-nessesary.
Now let's be theoretical and say the Stormcloaks prevail. Who will they trade with? Cyrodiil will cut them off so that dooms Whiterun, and High Rock still belongs to the Empire, so Markarth, Solitude, and possibly Falkreath can kiss all that money and matieral bye-bye. Hammerfell has all but fallen apart and is to busy dealing with the Aldmeri Dominion too worry about giving resources to Skyrim. Black Marsh and Elsewyre are too far, Morrowind is no-more and assuming it was operational would never lend aid to the Nords (due to their long rivalry).
So where does that leave Ulfric? It leaves him with a free Talos worshipping Nation full of hungry, poor, sick, and angry vagrants who want answers he isn't able to provide. Thus starting a revolution in the name of the Empire. It'll all come full circle people so save time, lives, and money and just go enlist in the Imperial Legion to crush these foolish usurpers.