The major flaw here: the Empire has to uphold the White-Gold Concordant which prevents Talos worship (and allows the Thalmor to enforce said ban). In the Elder Scrolls, if nobody believes a god is a god he ceases to be a god. This is a key step in the Thalmor plan to end the world and kill all humans.
Supporting the Empire is to support diecide, genocide, and armageddon, all at once.
It's really a very simple choice.
Not quite. Talos worship was never wiped out prior to the Markarth Incident, and it won't be even if the Empire control Skyrim. It's heavily implied that even many Imperial supporters still worship Talos. And even if somehow the Thalmor were able to stamp it out and remove Talos from godhood, the only way they could prevent Talos from coming back would be to ensure that they're never caught breaking the terms of the Concordat.
Also, while I understand they wish to avoid a Stormcloak victory, it is also known that the Thalmor's strategic goals would be
hampered by the Imperials winning the Skyrim civil war any time soon.