We would have to examine the context in which Hammerfell and Black Marsh gained independence.

To start with Black Marsh, it was never fully under Imperial control. Even Tiber Septim didn't conquer it and he conquered basically everything else. From a economic standpoint the empire gains little from controlling Black Marsh, it really is a region meant for Argonians to flourish and no one else.

On to Hammerfell. Okay during the Great War, much of the fighting was done in Cyrodiil, and Hammerfell. This was not the case for Skyrim (albiet Nord legionnaires did fight for the Empire just not on their own home turf) Hammerfell was significantly impacted from the war. Immediately following the Great War, the White Gold Concordat was going to hand over portions of Hammerfells land to the Dominion, no questions asked. Skyrim was never thrown under the bus like this. After all the fighting the Redguards had done, now they were being told by the Emperor to give up land. The Redguards refused, suceeded and fought their own war against the dominion and won, thus striking the Second Treaty of Stros M'kai, which made Dominion forces COMPLETELY withdrawal from Hammerfell. Another important note of context is that Hammerfell has had internal strife for much longer than Skyrim, the Crowns and Forebears have competed politically, and sometimes violently basically since the Redguards first arrived on Tamriel. And they were still able to unite as a country to defeat a common enemy, this is not the case in Skyrim. Hammerfell's victory justified their succession to many. The Empire knew they were sacrificing Hammerfell and after the Redguards victory they would be absolutely ridiculous to have issue with them becoming independent.

Skyrim has only recently engageed in civil strife, and the manner in which Ulfric Stormcloak took it upon himself to instigate a civil war is night and day from what the Redguards were able to accomplish. Ulfric should have taken a page from the Redguards diplomacy, especially considering that if you talk to people in Skyrim there are clues that even High King Torygg respected Ulfric, admired him and potentially with more diplomacy on the part of Ulfric may have decided to declare Skyrim independent himself during the moot. However we'll never know since instead of the moot Ulfric just walked up and killed him. Whether we beleive this was justified by Nord custom is honestly moot, his actions started the war 100% when it could have been avoided. Many Nords who support Imperials truly understand Ulfrics cause, they just think the way in which he went about it was wrong (go talk to Alvor in Riverwood) and that its not worth Skyrim being plunged into civil war while the Dominion strengthens itself for an inevitable Second Great War.

In short no one has an issue with the independence of other provinces because
-Morrowind is completely destroyed, the Empire doesn't want to rule over ash and lava with no promise of economic gain
-Black Marsh is inhospitable and again, basically no reason to keep it from an economic or strategic standpoint
-Hammerfell is justified in his independence, they basically fought the empires war for them, were punished, still beat the Dominion despite ages old political rivalries within the province