With even tacit supporters of Amaris banned the post liberation government was doomed to failure. The Hegemony could best hunt down these war criminals often competing with vigilantes but the planets of the nation seem to set their own agenda creating a basket case that Kerensky choose to leave. He again takes scorn for this action. I doubt he would press his own claim as First Lord which it seems he would have to do if you read this making it a much worse 1st Succession War. Me I’d go for neutrality as the Republic does in my AU if I were Kerensky and try to mediate the conflict. However he has now risen to such ineptitude that I doubt he or his buddy Victor could figure that out.
This is pretty standard stuff and makes pretty good sense. The final years of the Civil War were a bloody mess - politically, economically, socially, etc. If Kerensky really is upholding his interpretation of Star League law then there is virtually no way he was going to claim the mantle of First Lord.
Also, given is relative lack of political power in the High Council there was also no way for the Accords to be amended to remove the "Cameron as the First Lord" clause. Whoever would have inherited leadership of the Hegemony would have been placed in the position of ruling a battered nation without the benefit or protection of Star League laws or the Star League economy. Both disappeared when Richard II became worm food and Amaris's claim was rejected by Kerensky.
Kerensky was really in a bad spot. He could have remained behind, dismantled the SLDF, (because keeping them as the core of a new Hegemony wasn't going to happen) and became the next Director-General, but then the First Succession probably would have been worse. Again, remaining behind to mediate only works from a position of power and respect. Two things a Director-General Kerensky would not have during the First Succession. He's not Deborah Cameron, nor would he be leading the TH of Deborah's day.
Face it, no matter what, the TH's days were numbered after the Civil War.
Deamarisification swept the Hegemony afterwards with anyone supporting the Usurper barred from service in the new government. The way this is portrayed is odd to me as it again makes the SLDF sound as a bystander – weren’t they the government by force, i.e. military occupation?
As for the vigilantes. That's also fairly standard stuff. Reprisals and summary executions are the norm in recently liberated nations. It's usually the liberator or occupier government (note govt.) who then becomes responsible for stemming civilian violence and restructuring a new government. Use modern day examples in Iraq and Afghanistan to see how the system functions. It's important to remember two things here.
1. The working portions of the TH government were summarily removed from office.
2. The SLDF is an army, not an army with the backing of a civilian government.
Even in Iraq, it's not the US Army that's restructuring the Iraqi government, it's diplomats and civilian functionaries from the US and other UN nations. These are career government employees and politicians who specialize in, well...government. The Hegemony kinda of slits its own throat here. The SLDF is an occupying army or sorts. They can provide food, water and help with physical reconstruction but they haven't the skill sets or the foggiest clue how to run or rebuild a nation. Not too mention that despite being a part of the Star League, the Terran Hegemony is still the Terran Hegemony. It was founded and run by Terrans. The SLDF is not Terran. It's the peacekeeping force of the U.N. Sure there are Terrans in the SLDF, but there is a distinction.
We can also look to modern examples to showcase what happens when an occupying army refuses to work with the locals. Whether they're ex-Iraqi Republican Guard or simple town mayors, sweeping the old regime away can have devastating consequences. Restructuring and rebuilding a national government can sometimes be about making uncomfortable compromises. In James McKenna's case, he was faced with a slightly similar situation like Kerensky. He was an occupying/liberating army without a government. Rather than throw his finger eleven at the people running the old corrupt government and try to go at it alone, he simply restructured what was on paper (avoiding Civil War) and used the preexisting human resources (minus the really bad apples) to rebuild a new one.
The Post-Civil War Hegemony civilian population (and who allowed them to do this?) dumped any and all government personnel. These are capable experts, people with the skill sets necessary to hold an interstellar nation together and they were summarily dismissed. Not only dismissed, but hunted in some cases. Think they went along quietly or stayed in the Hegemony? Talk about a serious brain-drain.
Modern nation building has run into the same problems (and unsurprisingly TPTB draw the connection.)