It doesn't matter, that's what people the want. The Empire was happy to let Morrowind/Hammerfell do as they please, but like I said before you've come to the realisation it's a mistake and you need provinces so you'd rather have a Civil War then let Skyrim rule them selves. Skyrim is already isolated.. You said it your self, no legions occupy Skyrim, just "poor auxillaries" so what benefits do you offer apart from xenephobic views that all Nords are lawless barbarians?
If it was what the people wanted, there wouldn't be a Civil War. The Empire lost their holdings in Morrowind during the Stormcrown Interregnum/Red Mountain disaster. Titus II released Hammerfell because they refused the White-Gold Concordat, and the Empire was in no position to force the Redguards to accept peace. Morrowind suffers increased trading tax, they lost free trade when they went on their own.
It has nothing to do with "rather have a Civil War" it was Ulfric who set Skyrim down that path. Torygg was interested in hearing more about Ulfric's views of independence. Ulfric killing the High King and declaring war on the Western Holds in a move to kick out the Empire is hardly a diplomatic solution. It is Ulfric who keeps the Moot from meeting, so the Nords aren't even ruling themselves until Ulfric makes sure it is an easy win.
Skyrim isn't isolated, they're part of the Empire. Three united provinces, preparing for a second war with the Aldmeri Dominion. Stormcloak Skyrim is isolated, no allies and the Empire will most likely attack them. What are you even on about the Legions? I've said it myself that majority of the Legion is down in Cyrodiil preparing for round two with the Thalmor. The locally recruited auxiliaries are what is being used to try combat the rebellion. Titus II is keeping out the reinforcements. You honestly believe the people behind his death will want the Empire split in half? Vici's death is already framed on the Stormcloaks.
What benefits does the Empire offer Skyrim? Free trade, education, food, resources, military service for glory seeking Nords and Orcs wanting to explore the world or master their trade in smithing. Wealth for the Jarls to keep their cities in decent shape.
What do the Stormcloaks offer? Slavery, racial discrimination, xenophobic views to just worship Talos a bit louder? What happened to the Nords... They're turning more Imperial with all these visits to the temple. Last game they thought Imperials were uptight working and visiting the chapel always.
The whole "True Nords" thing the Stormcloaks go on about is really just another form of the "No true Scotsman" fallacy.
If this is the case, then Spain had no right to govern themselves prior to the Reconquista. For almost 800 years, Spain was not a unified nation with most of Iberia being taken by Muslim invaders. The reason why they couldn't kick them out sooner was because they were always waging wars amongst each other, but that's Feudal Europe for you when your vassals fight among themselves.
But, at 1942 when Iberia was finally in Christian hands, Spain and Portugal took it upon themselves to make fluffING EMPIRES THAT AFFECT OUR WORLD TODAY!!! It was great.
Comparing Tamriel to our world doesn't always work. Nords lorewise don't stay united for long, their conflicting nature ends up turning against them.
Now, you said there was a split in Skyrim... Right down the middle probably. Well, that isn't so bad. Sure, Skyrim has a history of fighting among themselves... But this is different.
Not really, this is the second time they're fighting against the Empire. Also the second time they're fighting for their independence. Stormcloaks are a Nord only focused movement.
Assume Ulfric and Tullius both die. The Jarls supporting Elisef (forgot how to spell her name) still support her. Anyone rising up in Ulfric's place would have to have a lot of his ideas just to keep the Jarls who had supported him to maintain the war, a war that is far easier without a competent strategist leading the enemy. If not Elisef will be made High Queen, probably unanimously.
But, being feudal, that doesn't mean half the Jarls won't petition her to break off from the Empire (something her husband would have done if Ulfric asked). So now, we deal with a lot of what ifs (a what if scenario I enjoy because Tullius isn't here to hold her hand). Feudalism is a curse, really.
Elisif isn't promised to be High Queen, she only has claim, same as the other Jarls. The Empire doesn't decide who becomes the next High King/Queen, the Moot decides. Ulfric was the one who wouldn't risk a Moot.
Tullius can be replaced easily, he himself even makes a comment in Season Unending that he would simply be recalled to Cyrodiil if he agreed to bad terms.
The Stormcloaks require Ulfric, they don't have anyone else really worthy to lead to them. The Jarls who support Ulfric, are very different minded. Laila doesn't have faith in Ulfric, Skald thinks Ulfric is the second coming of Talos, the Jarl in Winterhold seeks more authority for himself.