Vader as he was in Episode III obviously couldn't rule the Empire, even if he could kill Sidious.
Vader as he was during the Galactic Civil War obviously didn't kill Sidious because if he tried, he would get killed exactly like in Episode VI.
To be hϕnest, I have doubts that even with his reputation and experience of the OT that Vader could rule the Empire. Almost everybody in the entire Empire hated him.
"Grant Allen [...] had written a book about the Evolution of the Idea of God. [...] it would be much more interesting if God wrote a book about the evolution of the idea of Grant Allen." ~ G. K. Chesterton, The Everlasting Man