Hammerfell fought on at great cost, the entire southern part of their province was devastated. Redguards are also the most naturally talented warriors in Tamriel, but they couldn't have fought the Dominion to a stand still had it not been for the Empire. The Empire weakened the Aldmeri Dominion and that allowed the Redguards to fight a weakened Dominion, though it was at high cost, perhaps too high.
It's not just that Stormcloak Skyrim is unwilling to aid Cyrodiil, because we all know they won't rush to aid the Imperials, it's also because they will be unable to go into war. Their army is no match for the Aldmeri Dominion, they don't have the supplies needed to send soldiers all the way to Valenwood and Elsweyr, which will be where the war is. Not within Cyrodiil, nearly the entire army of the Empire is sitting on the Dominion's border, preparing for war. The Aldmeri are going to have a tough time getting into Cyrodiil with a united Empire, with Cyrodiil cut off from the other provinces that made up the Empire, it's going to be a lot harder.
You talk about the provinces forming an alliance... They're already in an alliance, the Empire. You're breaking apart that alliance. You don't break an alliance to form a new alliance which would be the exact same as it would be if the Empire had remained united and attacked the Aldmeri Dominion. The Talos ban isn't permanent.
You want to fight the Aldmeri Dominion, taking the war to them, join the Legion. Looking at the big picture.
You want to kick out a few Thalmor Agents by sacking two Nordic cities and slaughtering many Nords to put Ulfric Stormcloak on the throne of Skyrim, while he and the rest of the Stormcloaks boast about attacking the Aldmeri Dominion, but really they can't, spending rest of their lives being all talk. Join the Stormcloaks. Looking at the small picture.
At least the Empire is in a better position to attack the Aldmeri Dominion, by having their Legions already deployed along the Dominion's border, preparing for a war.
Main Stormcloak argument is that the Empire are Thalmor puppets. Yet none simply ask, why like twenty six years later do the Thalmor start trouble? They have had twenty six years, it's not like the treaty was made yesterday. Why this sudden tactic to distract the Empire, to force them into a Civil War. I mean if the Empire were simply puppets, why would they be seeking the destruction of the Empire, what could of made them go to this length to deplete Imperial resources. I guess the appearance of nearly the entire Imperial Army on their doorstep made them go "Oh plops"