Imperials vs Stormcloaks

Then you'd just be supporting the Thalmor.

The Imperials don't really have one either.

It's basically "Let's deal with this one problem, then we can prepare for the other problem" versus "Let's grab our ankles and hope everything works out". Neither is really a viable strategy.

Though it's also implied in the narrative that the Nords were winning most of their battles during the war with the Thalmor, and it was the Imperials who folded, so in a scenario where Skyrim goes independent there's always the possibility that the better fighters having to defend a much smaller region means they'd win any war against the Thalmor (so long as they weren't constantly being bled by the Empire at the same time). Same goes for the Redguard, who were basically doing an effective job of fighting back against the Thalmor until they were sold out by their own allies (which is a significant part of what prompted Skyrim to rebel in the first place).

That's the main reason why the Thalmor don't want either side to win the civil war. The longer the Imperials fight the Stormcloaks, the weaker each faction gets, and the easier it will be for the Thalmor to maintain their own powerbase (or expand it). Either side winning solidifies powerful opposition that will be far better equipped to oppose the Thalmor.