And the Empire betraying Hammerfell weakened Tamriel.
If the Stormcloaks were victorious then they would cease all trading with the Imperial-financed East Empire Company. If you talk with traders in many towns or cities they refer to how important that trade is for Skyrim. Infact, the Emperor's cousin owns and operates the company from Solitude. If the Stormcloaks succeeded in establishing Skyrim as a separate state then there would be no trade between them and the Empire, creating a vacuum of income for coastal cities.
Additionally, if Skyrim were to remain in Imperial control, it would be much easier for residents of Tamriel to migrate there. This would create new business and reduce unemployment. Perhaps more traders could establish shops in Winterhold to save their problems. Think of it as like the Eurozone. It's much easier for someone from France to move to Germany than it is for someone from America to do so.
If the Stormcloaks were to succeed then they would have to change the currency. Presently the Empire uses Septims, there is the possibility that Ulfric wishes to create a more Nordic identity for Skyrim and thus there would be a changeover of currency. This could result in widespread financial problems (See Weimar Germany)
It can be discovered in a dossier from the Thalmor Embassy that Ulfric Stormcloak is a Thalmor asset, and has been for a considerable length of time. Although he is dormant, they have the ability to contact him (despite it being 'high risk'). If the Stormcloak rebellion were to succeed, then it would seem likely that the Thalmor would be able to subvert Skyrim's funds and use it to further their 'racial cleansing', creating a significant drain of resources.
As you mentioned, the Stormcloaks seem to be overwhelmingly racist. They hate elves and also mages. If the Stormcloak uprising continued, then these individuals could face persecution. Thus, there is the possibility that elves and mages leave Skyrim en masse, taking their business with them.
So overall it's better for Skyrim economically to remain as a semi-autonomous Imperial state.