it doesn't make sense.. "conclusion" is not what doesn't make sense, after everything Ulfric did the empire suddenly allying with him is what doesn't, and even then they wouldn't have the man power..
maybe you will understand if i make a real world comparison..
say I rallied a group of my fellow Canadians, we killed or exiled every politician that didn't submit to my will within Alberta (I am not from Alberta, i am simply using it as an example), wiped out every Military Official and base within the province, and shot down a plane with the prime minster aboard as it flew overhead.. afterwords, i declared Alberta a sovereign nation..
in that scenario, do you think it would be realistic for the Federal Government to say "ohh sure, thats fine we don't mind.. ohh, but how about you join us and we cross the border and wipe the US off the earth, we don't have what it would take, but it would sure be cool if we won!".. no, they would send in the rest of their military and allies (probably including the US) and run me into the ground, or keep fighting until they no longer could..
what your suggesting is essentially the same thing with a TES coat of paint, thats why it makes no sense within the setting.. your asking for something that makes no sense simply because "it would be cool".. once again, you advocate for great writing, but you openly ask for the opposite due to "rule of cool"
as for your comparison with Oblivion, the Oblivion crisis was the games main story.. Skyrims Civil War isn't, Skyrims story is about the return of Dragons and the World Eater, the Civil War is just something going on at the same time..
and even then, the Dominion is not a Belligerent in the conflict, the Conflict is between Ulfrics Rebellion, and Imperial Loyalists.. the dominion is not part of it, they are not directly aiding either side, they have an embassy and a few officials in the province. if that makes them part of the conflict, I guess half the western world is responsible for the situation in Ukraine.. invading the Dominion to End Skyrims Civil War (you do know what a Civil War is, right? even by the very definition the Dominion isn't involved) would be like invading North Korea to end the Syrian conflict..
btw, there were many questlines in Oblivion (and even Morrowind) we never got full conclusions of either, because they were side quests and not the main one.. once again, Skyrim is not about the Civil War, its about Dragons..