The original Star Wars trilogy famously climaxes with Darth Vader redeeming himself by (apparently) killing the Emperor by throwing him down one of the deep shafts that appear to be a staple of Imperial architecture and mortally wounding himself in the process, but the context of the Prequel Trilogy raises the question of why he didn’t do this sooner.
Although now relegated to the Legends continuity along with the rest of the Expanded Universe, the novel Dark Lord: The Rise of Darth Vader explores the rising to prominence of the newly-minted Empire’s black knight following the events of Revenge of the Sith. It details the internal conflict of Vader as he attempts to bury the identity of Anakin Skywalker and embrace his new destiny of a Sith Lord and disciple of the Dark Side, lest he be driven insane by the duality tearing his mind apart.
After Vader learns what happened to Padmé, the person who everything he did was to save, you would think that the loss would have motivated him to kill Palpatine out of vengeance. Indeed, the novel states that had he defeated Obi-Wan on Mustafar he would have then set his sights on the Emperor in revenge for how much he had been manipulated, and may well have succeeded.
Although Vader didn’t possess as much as raw power as the Emperor in wielding the Force, he was far more skilled in lightsaber combat, but with the critical injuries he sustained in his duel with Obi-Wan – having one arm and both legs severed and being left to immolate in a rising pool of lava – he was left in no physical condition to take on the Sith Lord. Subsequently, after his life was extended and physical form restored by cyborg enhancements, he remained psychologically broken by his ordeal, forever reminded that his power remained a shadow of what it once was.
It took twenty years and seeing his son being sadistically tortured to break through the self-imposed mental conditioning and for a fragment of his former self to return, settling the score long lingering and in the process, freeing the galaxy from the grip of a tyrant and reconnecting himself with the Light Side at the moment of his death.
All the way back to The Empire Strikes Back, Star Wars has been continually retconning itself, replacing original plans with better ideas and justifying inconsistencies. And although now unofficial, the explanation of Vader’s hesitance is another facet of an iconic character already richly explored.