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.
"There is something going on in time and space, and beyond time and space, which, whether we like it or not, spells duty." -Winston Churchill
"For of all sad words of tongue or pen, The saddest are these: 'It might have been!'" -John Whittier
"Apathy is death." -Kreia