Shouldn't have done that, just wasted my free time on some random thread because
i must prove why i'm right and everyone else is wrong and smell bad.
Looking at the subject from a lore point of view rather than game mechanics, otherwise the pirate-zombies are the obvious choice as they found the secret to instant-cloning and matter-creation.
Short version:
-Indy: Not viable alone
-Pirates: Not a government
-Path: Can't be too big
-Church: Stagnation and potential strife ahead but at least stable
-Diktat: Only viable in Askonia
-TT: No interest for them at all
-PL: Need the Hegemony as a credible threat
-Hegemony: The only one who actually want to expand
LONG VERSION
Spoiler
The Independents are only so because of a status-quo in a multipolar sector, the moment this situation end will result in drastic governmental changes.
They have no unified anything, it's a mess that only hold because the sector itself is a mess. Their unity and legitimacy in rule would be almost non-existant, corruption and piracy would be rampant. Destined to blow up again and/or get absorbed in an actually sensible regime.
The pirates are not a proper form of government, "Pirate Republic" is a meme. Piracy rely on the existence of proper governments operating trade and a significant discontent in the common people, which is drastically exacerbated in times of war. They are currently living their golden age, it can only go down if the situation either improve or deteriorate further.
The Path while definitely able to hold territory as it already do, would collapse if it ever achieved victory, due to it's foundational aversion to advanced technology (including antimatter-fuel itself). The hypocrisy couldn't stand without an enemy to justify against, and it'll either dissolve into anarchy, dictatorships, or tone down in it's beliefs closer to the level of the Church.
The Church while economically inefficient and somewhat corrupt, at least possess a stable social structure that anchors itself into it's citizen belief, legitimacy is on their side as long as the gates stay shut. However stagnation is all that is waiting without technological advances or already existing Domain relics.
Schism is also a threat, reinforced by Gilead being too good for the Church's own good, everyone would want it for themselves as it is currently VIP ground.
The Diktat is what it is because of the Askonia Crisis, it's an isolationist military dictatorship. Legitimacy is held in Askonia, it's even in the name: Sindrian Diktat. There's no intent to expand in the first place otherwise it wouldn't be the Diktat anymore.
TT is a megacorp, which are not functional governments period. It'll need another regime to live into just like the Domain days.
It is simply not beneficial for TT to rule over large populations, reason why they're less than 1% of the sector in the first place and can afford to massacre heavily populated worlds to further their goals.
And i swear if the ruler is some moustache-twirling-and-i-must-scream evil AI i will personally gather every core in the sector and force them to review internet fanfictions until the last star cease to radiate onto the universe.
The League, we're told from the beginning that what they love is not freedom from the Domain. It's the freedom to rule their population themselves, as in "How dare you take the power that i rightfully seized".
They most likely don't even want the Hegemony to disappear, it's the reason why the League exist in the first place, and a god-sent regarding citizen approval toward the regime.
While the different governments may stand, the League will dissolve once every existential threat is dealt with, and of course turn into each-other as everyone now need a new enemy to stay in power.
Would however be dreamlike soil for TT to live on.
The Hegemony is the only one with a clear expansionist drive. It's doing incredibly well for a provisional regime, and while Chicomoztoc is not a nice place to be, it would have been far worse in any other hand due to the sheer task of taking care of such a massive population on such a mediocre world.
The Hegemony itself is still a weird state, as it's an army living on top of governments they stabilized/toppled over and rely-on.
The command structure is solid (Askonia was the exception, as the guy in charge saw THE opportunity and took it).
Stability is good as long as you look away from the big industrial ball of despair.
Legitimacy couldn't be higher, + currently maintaining ties with the Church (question is if they stay once TT is dealt with).
AI will be kept in check for a long time as it's almost entirely TT assets (fully expect those rascals to go order 66 on our arses in a future release) but technology as a whole doesn't suffer an aversion.
Having the military lay down a proper ruling system and getting them to do something else than warfare will be the highest challenges to face, if managed we get to have discount Domain that cleans-up the sector and actually experience growth.
Overall the least likely to ***-up and collapse miserably right after victory, and if the PC is actually an exceptional and influential character, could steer the whole thing in a more desirable direction (for whoever in this thread said that shots are a step above humanity's survival regarding order of importance).