The problem is the Thalmor. The war should be against them. Should be an option to take them out.
Give it time, Bethesda was never going to give us a game where you save the world from dragons, greatly influence the outcome of a civil way and topple another world power.
I'd say they are building to a more Thalmor centric storyline, considering the growth of their influence in the world from Oblivion to Skyrim.
As for justification of this war...yeah, it's a good enough cause. Nords and Imperials alike fought in the Great War and during the Red Ring battle, both the Thalmor and the Legion were destroyed. Now, Titus has the Thalmor retreating. What does he do? Sign over the Empire to a force that's just as weak as them. That's the logical equivalent of you and another person fist fighting and when both of you are downed, you slit your own throat.
Wait, if both are downed, one wouldn't have the other retreating, at least not by a significant margin. As I understood it anyway the Thalmor were still is a somewhat stronger position, which is why the Empire accepted the treaty even though they had a bad feeling about it - it gave them a chance to regroup and rebuild and get ready for round two.
However, Tullius really does seem like a Thalmor sympathizer since he himself restricts Legate Rikke from any worship of Talos as seen when you kill Ulfric.
If he is a Thalmor sympathizer he is good at hiding it, since he really comes off as being quite against them and fully prepared to fight them in the next war he believes is coming. Of course he is loyal to the Empire and the laws which includes that which the Empire agreed to with the Thalmor, so it probably wouldn't do to have Rikke be seen disobeying them.
However, again, Stormcloaks are 100% guaranteed to fight the Thalmor and has a high chance of defeating them while the Empire doesn't have either qualities.
I think the Empire mainly wants to fight if they have a chance to win and want to buy time till that is possible. Not sure why Skyrim alone (and under Ulfric probably not going to well utilyze the potential of non-Nord races) is going to do better against the Aldmeri Dominion then an entire united Empire.