What killing King Charles actually accomplishes is that merely Lelouch has one less enemy so he can focus on stopping his brother Schneizel, who represents a much more competent threat than his father did, one with the connections to build the Sword of Damocles...
There is two problems with this conflict though. Firstly, the way that Lelouch built a resistance against his brother was not to win back his old allies and prove to them his trust worthiness, but by magically flip the whole chessboard and turn every Britannian into a mind slave willingly do his bidding. That sounds exactly like liberal fantasy fixing the system and transform it into a force for good. Secondly, Schneizel also did a board flip and get everyone on the rebel group to support him as their leader for a war which essentially is just a fight for the throne of the world. The rebel even complicit in a nuclear first strike attack on the Britannian capital which have unknown number of civilian in it.
Now, the very existence of geass magic fundamentally divorces the world of Code Geass from ours, but I thought the Black Knight reaction to Zero’s identity and the power of Geass made a lot of sense...
This plot point however shine the spot light on the structural problem of the whole rebels. They are just a bunch of people with no unified ideology that can let them look pass the fear of the power of geass to even offer Lelouch a chance to explain himself. They don't even offer him a real trial before trying to gun him down in cold blood. While I'm sure there are many example in real life where people flipped out and assassinated their political leaders for less. The story decision here to let Lelouch be saved not by the quality of his ideology, or any of his policies but just purely because another broken and exploited character clung onto him and bailed him out with their life speak a lot for the quality of the rebels leadership and ideology.
That's my main problem with Code Geass to be honest. Overall, it's an entertaining show with the facade of anti-colonialism, anti-imperialism, pretty twisting story line and some awesome mecha battle. However, the show stop short of offering any true solutions to the problems and instead just outright prescript great person theory and enlightenment dictatorship to imperialism. It doesn't even have any representation for communism, anarchism or any more leftist groups. Instead, we had an imperial capitalist monarchism vs a bunch of nationalist monarchist of a different religion vs some liberal democracies in the background.
Most of the time the platforms are already in capitalist hands so it's really easy to just ask them to self moderate to ban and evict the left. The they just boost the "center" and voila!