I'm going to go ahead and list out a couple things, that may or may not have already been covered. But I figure its better to have a nice round-up and some general clarification on events:
Talos has to be worshiped. Otherwise, he'll go poof. The gods divinity, and especially the divinity of Talos rely on mythopoesis. IE, they need people to believe in them to really give them power. The Thalmor push for the worship of Talos being banned because they don't see him as a god, and whats worse, they see him as an insult because it shows that a mere human could reach divinity while all Altmer are still stuck as mortals. Further, they want to return to the point where they weren't mortals. Removing Talos (by way of eliminating all those who believe in him, and castrating him in those who could come to believe in him) is the first step towards that. The Thalmor ultimately want to end the world for humans (and thus reverse the creation of Mundus) because then that would (according to what they think will happen) return them to a point before Mundus was created.
Ulfric started his rebellion because he was denied the ability to openly worship Talos by the Empire, and not only that, but he was thrown into the hands of the Thalmor shortly afterwords. For merely doing what he was asked by his Empire and asking for what he was promised. While the Thalmor call him an "asset", its quite foolish to assume that after being tortured by the Thalmor that he's going to just get all buddy buddy with them. No most likely the Thalmor heard him cursing the Empire and vowing some sort of revenge while being tortured (or while in his cell) and as such saw fit to let him escape to start his Rebellion. They say that they go on to establish contact, but again, its foolish to assume that he'd just buddy up to them after what happened. No, most likely the Thalmor have a plant in his army that is working towards sustaining the war while also undermining it. I personally suspect his steward, but it could be anyone.
This however doesn't make his rebellion a bad thing.
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The current Empire needs to die. Its higher leadership is plagued by incompetence and corruption, its Emperor (who was a bloody short-sighted idiot, more on that in a second) is about to be assassinated, its military can't hold onto its one major holding outside of Cyrodiil (High Rock is currently too busy fussing about themselves to be much a bother to anyone), and whats worse its not even a legitimate Empire. The Throne was taken by force by the first Titus Mede, so the Empire you all think you're supporting actually died off a little under 200 years ago.
Its ineptitude is proven in its actions. When it first began, it failed to respond to what was occurring in the Empire. The entire south of Tamriel was lost in the time leading up to the Great War, Morrowind was torn apart, and western Tamriel went to war against Orsinium, which eventually lead to that city being destroyed yet again, breaking the treaties that existed there and ultimately going against the Empire's rule. But sure, may be you can give the Mede Empire a break here because it was "weak". That's fine.
Then the Great War comes along. The Dominion gives the Empire an ultimatum, and demands the south of Hammerfel and several other things that would basically cripple what was left of the Empire. Mede II has the sense to deny them this. The Dominion then proceeds to invade within a day of that ultimatum being denied, ultimately circumventing Cyrodiil's defenses, and passing straight into Hammerfel, with the intent on taking it. (Cyrodiil being invaded was just a ploy to keep the Legion divided) Cyrodiil proves to be easier to take, with success being had by Narafiin's army at an impressive rate. This leads to the point when the south of Hammerfel is taken, and the Dominion's separate army (separate, remember that) moving across the Alik'r desert to be stopped in Skaven. At this point, the Dominion calls on all available forces (which basically means any forces not currently sitting in Hammerfel or otherwise being used for law and order) to march on Cyrodiil to capture the Imperial City and in turn overthrow the Empire altogether. They capture the Imperial City and begin slaughtering the inhabitants of Cyrodiil save those who live in the northern areas, namely Bruma.
Eventually, the Legion manages to rally itself into coherence, and the Emperor orders the Legion in Hammerfel (along with Legions coming out of Skyrim and High Rock) to march on Cyrodiil, which ultimately would have left Hammerfel at the hands of the Dominion's invasion force there. But General Decianus has a brain and leaves troops there who go on to form the core of the army that would continue fighting there. So, the Legion marches on Cyrodiil, attacks the Dominion held Imperial City and retakes it, destroying the vast majority of the Dominion's entire army along with it.
Then, inexplicably, Mede II signs the White-Gold Concordat, which completely negates the fact that the Legion destroyed the Dominion's army by giving the Dominion virtually all of the main awards they wished to gain in the first place with their ultimatum. This is ultimately proven to be one of the stupidest decisions an Emperor could make, as Hammerfel (which is left to the wolves because Mede is a short-sighted dillweed) goes on to fight the Dominion's invasion force (which was built specifically to take Hammerfel, and the Thalmor would not have been so stupid to put a force together that couldn't have taken Hammerfel) to a total standstill on its own (using a diminished single Legion and whatever militia they could have raised) and kept the Dominion in this standstill for 5 years afterwords, at which point the Dominion gives up and lets Hammerfel have all of its lands back.
This shows us that the war could have been sustained with little problem to the Empire. For one, Hammerfel was already going to be involved in war, so there's no point stopping war for their sake. High Rock and Skyrim never saw the war and at that point would never have seen the war unless the Dominion somehow found themselves a magical mcguffin. As such, stopping war or continuing it wasn't going to put any more strain on them. Cyrodiil was the only place that would have truly had a reason to see the war stopped (and note that this is important to note for later) and even then, the remaining Legion forces that could continue to fight would have been able to defend Cyrodiil's southern borders, especially when complemented with fresh troops from the two provinces up in the north that never saw the war and were never drawn on for fresh troops. (The legions that were taken from the two were already established there, well before the war. They weren't new troops going off to their first fight) It would have been the same for resources. High Rock and Skyrim could have easily supported Cyrodiil and the resistance in Hammerfel with proper rationing.
The mere fact that the Dominion gave up fighting against one single province shows that they would not have been able to sustain a war against the rest of northern, western, and central Tamriel. Elsweyrs status as a pair of client states to the Dominion wouldn't have helped them, because the Khajiit proved that they weren't going to go to war for the Dominion, both in their actions during the Great War (where their only presence was in allowing Dominion troops asylum) and afterwords, where they never sent help to Hammerfel's invasion force.
But no, Titus Mede II signed the WGC and completely undermined the victory he just had against his enemy, and all for the seeming point of serving CYRODIIL's interests. The Empire clings to Skyrim because it knows that Cyrodiil will be left to the mercy of the Dominion (though even then, the Dominion can't successfully invade anyone at this point, and wont' be able to for at least a hundred years. Best case scenario they knock over the Empire, but thats not saying much when it would just leave them with a weak grip on Cyrodiil), not because Tamriel will fall. Not because the Dominion is some mystical force thats just ready to destroy the Empire but is only holding back because of some stupid treaty. Not because Cyrodiil actually cares about Skyrim.
The Mede Empire is weak, has always been weak, and has shown that its even willing to sell out the most important god to Mankind all for the sake of sparing poor old Cyrodiil the threat of war. It needs to die, so that something new can take its place. Something that can, and will stand up the Dominion and won't just fall apart soon afterwords anyway. The Mede Empire will never be able to regain the allegiance of Hammerfel, as Hammerfel would not ally themselves with the very force that sold them out to the Dominion, unless by force, which would result in war even more detrimental than the current Civil War in Skyrim. And the allegiance of Hammerfel is going to be crucial for whomever decides to go up against the Dominion. Its sea access and key experience with the Dominion is invaluable, and the Empire will never be able to touch it.
It needs to die, and a unified Skyrim coming to call upon the rest of mankind (and much of Mer-kind for that matter)on Tamriel is going to be the best hope against the Dominion when the time comes.
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Those saying that the enforcement of the Talos ban only being started after the Civil War are, well stupid, because they're missing the point entirely of whats occurring. Sitting there and worshiping in the darkness (in some petty attempt to stay alive long enough to see an end you can't escape) is just as bad as outright accepting someone telling you can't worship X god anymore. The Thalmor want to obliterate Talos and by extension the rest of mankind and the entirety of Mundus along with it. Worshiping in secret will do NOTHING. It will only postpone the inevitable. The Thalmor might not have been so active in Skyrim before the Civil War, but you damn well know they were going to be at some point regardless. They want to obliterate Talos. Left unchecked, they WILL start purging Talos worshipers in Skyrim, Civil War or not.
I can tell you as a real-life follower of a polytheistic religion that an invasion force coming in and telling me I can't worship one of my gods would easily make me want to rise in rebellion. The fact that there are many gods does not make it any less terrible when you're told you can't worship one of them. And if that god is the most popular one in the bunch? Oh, its bad.
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As touched on above, while the rebellion is indeed beneficial to the Dominion, that does not automatically make the rebellion a bad thing. As stated above, the Empire needs to die. And as the dossier on Ulfric shows, their rebellion succeeding would be just as detrimental to them as it would be if the rebellion was put down in a timely fashion by the Legion. The Thalmor need to be dealt with yes, but they aren't some magical power that's just waiting to waltz over and destroy all of Tamriel. They actually can't.
Their army is diminished still from the Great War. Valenwood can't be called on for support because not only does only a small portion of the population there actually support the Thalmor government, but those that don't support it are being purged still, 200 years after Valenwood was seized by the Dominion (They never joined willingly). Valenwood is on the verge of civil war itself, and even that civil war never erupts, the few among the Bosmer that will go to war for the Dominion are not going to give the Dominion the forces it needs to take on the rest of Tamriel. Elsweyr can't be called on, they won't go to war for the Dominion as they've shown on two occasions already. (and they can't be forced to either. Learn what a client state is)
The Dominion would need at least 100 years more to prepare before it could hope to take on the rest of Tamriel, but even then, they'd have a hard time because by then, no matter who wins the Civil War, the Dominion is going to have an army on its doorstep. And as I showed above, a Skyrim-lead army is going to be the best option, as it will then lead to a better future for Tamriel, and not one lead by the same inept government that allowed us to come to be in this mess in the first place.