Will people please stop saying an Empire "unites" anything? It is not unity to wipe out armies, kill nobility, and smash cities. Subjugation is not peace. This is not the Republic of Tamriel, but an empire.
Well, what would happen if the Thalmor threat got resolved (no matter by whom) and the Empire stepped down from the de facto ruler position?
There is two options here. The regions could either start a massive war with each other, destroying Tamriel in the process of holding this no holds barred fight, with an everyone against everyone basis until there's only one left OR they can shrink into themselves, closing down borders, trade routes and basically everything, deciding to never interact with each other / never aid the other region and keep whatever resources, military power and wealth they have only for themselves.
I guess the Argonians could fare quite well, Black Marsh has always been independent. The Altmer's homeland seems like it can accomodate their needs. After a little patching up, Cyrodiil is cool too. What is going to happen to the others? Orsimers have no land of their own. Vvardenfell got blown to pieces. Skyrim -even in it's glory- is cold as [censored] and barely anything survives the harsh climate aside from pine trees and bears. High Rock is small and the rocky cliffs, hills and mountains are a sure way to never succeed in growing and maintaining plantations.
While Valenwood is nothing short of awesome, the Green Pact makes life kind of really friggin impossible for Bosmers without the ability to trade with others. Elsweyr is like Skyrim but instead of harsh cold, you get harsh hot and a sh*tton of dry plains with the occasional patch of a jungle or two. Hammerfell just got over some pretty hardcoe Thalmor raiding, they won but it had cost them tremendous amount of money, supplies and life.
If no one steps up to the position of supreme ruler of Tamriel, it can get out of hand really, really quick and end up doing what the Thalmor wanted: end Tamriel.