Why didn't Yoda and Obi-Wan Kill Darth Vader and Emperor Palpatine?

Despite the strong will and efforts displayed, Yoda and Obi-Wan Kenobi did not manage to eliminate Darth Vader and Emperor Palpatine from the Star Wars universe. The reason for this is not a lack of trying, but rather a series of strategic and logistical challenges they faced.

Strategic Options

Obi-Wan and Yoda had to choose from three strategic options:

They ultimately chose the third option, splitting up so that Obi-Wan could face Anakin/Vader on Mustafar and Yoda would go to Coruscant to confront Emperor Palpatine. They made this decision after careful consideration of various factors, such as the power dynamics and available resources.

Why They Split Up

Obi-Wan wasn't strong enough to defeat Sidious even with Yoda's help, and they only had one chance. They needed to maximize their chances of success, and their knowledge of where both Sith would be enabled them to choose the optimal strategy for eradicating the Sith.

Obi-Wan’s Decision on Mustafar

When Obi-Wan left Anakin to die on Mustafar, he failed to kill the fallen Sith. This decision was made due to the harsh environment and the fact that Anakin had become a sentient being resistant to fire and lava, which would have made instantaneous elimination impossible.

Yoda’s Battle Against Emperor Palpatine

Yoda didn't manage to kill the Emperor because of his weakened state during the battle. Despite using Tutikamis (a form of Force lightning shielding), Yoda's hands were significantly injured, and he lost his lightsaber. In contrast, Palpatine emerged relatively unharmed, having been thrown back over a senate pod.

Furthermore, Yoda's power had diminished since the dark side nexus, while Palpatine had grown more powerful through dark side experiments. In a rematch, it is almost certain that Palpatine would win regardless of Yoda's original strength.

Strength and Experience of Darth Vader

Darth Vader had become weaker compared to his former self, but he had gained significant experience and control over the Force. His saber skills had improved, but so had Obi-Wan's. Both masters had become rusty and weaker: Obi-Wan on Tatooine and Yoda after his battle with Palpatine.

However, the main challenge was the security and protection the Sith provided themselves. The two Sith had an army, meaning any attempt by Yoda or Obi-Wan to get near Coruscant would result in their ship being destroyed, leaving them unable to reach either the Imperial palace or Vader's sanctuary.

Ultimately, while Yoda and Obi-Wan faced significant obstacles, their strategic approach and the overwhelming security provided by the Sith made their mission to eliminate the Sith nearly impossible.