The Thalmor couldn't just waltz around doing what they wanted, they're using the Civil war to do it. Lack of Imperial control gives the Thalmor free reigns, the Empire can't fight a Civil War while watching the Thalmor.
Head to Markarth, speak with the head of the Justiciar's (The Talos hunters) he asks you to break into someone's house because the Empire supporting Jarl won't call for his arrest.
Look at the Justiciar execution orders when they send them after you. 'If caught by local authorities, we are unable to offer you any assistance.' Imperial soldiers will even attack the Thalmor if they try to kill you.
The Thalmor make use of Nord assets and Khajiit assassins. The Thalmor aren't the only group known to wage secret wars, the Empire does it also. Tullius himself is using Agents in Skyrim too. More than likely the Empire is doing the same thing to the Thalmor, both sides attacking from the shadows. The Empire doesn't just fight with the Legions, they make use of all forms of warfare
If you believe the Empire are just blind and sitting around playing with their thumbs, you need to read more about what the Empire exactly gets up to on the shadow side of things.
yet, what is to stop the Thalmor from assassinating the Elder Council? What is to prevent them from winning the next great war without fighting it?
I never said blind? By "not knowing it is a shadow war" I meant that the Empire does not realize the true threat of the Thalmor comes from them having agents in the Empire, not just in terms of the legal parts. Them being in Skyrim because of the Civil War is part of that. To get the Empire to legally let them use the WGC to eliminate threats to the Dominions war against the Empire. They are either lazy or incompetent for not fighting the thalmor on the Thalmor's terms and ignoring Ulfric. The Empire and the Thalmor arwe the reason he wants to break away from the Empire, not for power's sake.
IF the Nords truly thought Ulfric was a murderer and traitor to the people of Skyrim, they would not be joining him to fight for THEIR freedom.
What is stopping the Thalmor assassinating the Elder Council? Oh, about thousands of soldiers.
Empire should be ignoring Ulfric? Ignore the fact that Ulfric has raised an army and is attacking the Western Holds? Your solution is to simply ignore Ulfric and his rebellion... really?
The Empire is aware the threat the Thalmor pose, far more than the Stormcloaks. Many in the Legion mention the threat the Thalmor pose. The Thalmor couldn't do what they wanted pre-Stormcloak rebellion. They couldn't arrest anyone they wanted, they couldn't drag people out in the middle of the night.
Thalmor had to have complete evidence, hell it took them seven days of someone shouting about Talos in Markarth (Where the head of the Justiciars is based) to arrest him. They couldn't touch those who worshiped in secret, couldn't touch anyone they wanted.
Nords are joining Ulfric's rebellion for many reasons, one is "Cause I'm a true Nord, simply as is" the other is about his/her cousin being snatched in the middle of the night by the Thalmor (Who can only do that because of Ulfric, because he gave the Thalmor the excuse they needed and wanted). But not all Nords are joining Ulfric, many are joining the Imperial Legion also. Many do call Ulfric murderer and traitor, they join the Empire.
Why do you think the Thalmor call Ulfric Stormcloak their asset, because he is doing what they want, he is allowing them to cause as much grief to the Empire as possible. The only Thalmor puppet is Ulfric.
Ulfric wants the throne for himself, don't give me the "But it isn't for power, honest." Ulfric killed Torygg who actually liked and respected Ulfric and would have probably been willing to most likely go independent had Ulfric asked him. "With us or against us" Yeah, true words of freedom.
Since when is racial segregation and slavery the pillars of freedom?
"We will do whatever I decide is in the best interests of Skyrim. Are we clear?" - Ulfric Stormcloak. Completely the sign of a non-oppressive government...
Seems to me Skyrim is heading for a proper dictatorship. Ulfric has his armies in the cities and Galmar keeping the Jarls in line, making sure they follow orders.