I like this idea.

Excellent idea.  I suggest that a range of rebellion outcomes also be enabled by the game engine.  From a simple, 'rebel groups are gaining followers on planet <name>.'  and..  'Large sectors of general population are sympathizing with rebellious' groups demands.  and.. 'Covert affairs liaisons suggest possibilities of some military (ground?) (Naval) forces sympathizing with rebel demands.' and .. 'Colony in critical turmoil as dissidents occupy seats of power.'  to..  'Planet <name> has declared independence from <our empire/civ>'  Fleet(s) <name> have joined the new government of planet <name>.'  This escalating set of communiques from the rebelling planet along with possible fleet defections (patriots) would add great flavor to game.  Also, include real diplomacy options.  Rebelling planets become subject to various interventions, an active, interesting set of unfolding choices and consequences for dealing with their relationship with Central government.  A colony world that is beginning to exhibit signs of dissatisfaction with the central government might be won back by agreeing to some/all the demands.  Do they feel they are paying too much to the general treasury?  <lower taxes>.  Are they losing too many civilians to raids by 'others?' <increase patrols/protection>.  Have too many of their own soldiers/sailors been killed in recent combat way out there somewhere? <address excessive causalities>.  What think you?

Maybe even have the ability to start playing as one of the rebel factions..

Would be kinda cool to lead rebellion against an established Civilization.

Maybe even have a game simulated out until there was a rebellion, and then you pick up from there.

Would be a nice challenge.

I too think this is a good idea.  I don't know how realistic it would be to begin implementation at this point in the production cycle, however if it is already planned for it could be realllllly cool!

What about Starbases?  How do they fit into this discussion.  They don't secede, but once they amass enough modules, they achieve a city-state status.  When a race is conquered, the Starbase just disappears when in fact that would not happen.  A huge hunk of metal just doesn't disappear if it's civilization is conquered and the Starbase is untouched.  Wouldn't it remain in space and become an independent state?  Unlike ships from conquered civilizations becoming pirates, a Starbase has more to offer especially in it's ability to become an independent entrepreneur.  Shouldn't there be these same politics in dealing with these new identities?

Me think dis: frequency of "disturbances" should be directly linked with "freedom" of political system we have - the less free that system is, the fewer chances fo any form of disturbances. I.e. if we have Imperial government, then we won't have rebels. If we have democracy, then we have a lot of those, should something went sideways.

No, I mean disturbances affected from outside. Like when you build influence stations and start broadcasting "our jeans are better than yours!", resulting into "Origin sucks, we want better sales like Steam does!"

Yeah in a democracy the ruling party often, but most totalitarians have regular change in leaderships. When I mean leaderships this way I mean ones that have no connection with each other.