Luke Skywalker's redemption of Darth Vader defeated Palpatine, but the galaxy didn't need a Jedi to vanquish the Sith.
Palpatine thought the Jedi were his only hope, therefore he tried to destroy them. Few Jedi escaped Order 66, and Darth Vader and his Inquisitors hunted them.
Palpatine's genius was weaponizing the dark side. Every person in the galaxy contributes to the balance of the Force, and every choice tips it toward the light or dark.
The Emperor constructed a system that encouraged self-interested choices, and he positioned himself to benefit.
Palpatine didn't fear the Rebellion because even the Emperor's opponents attacked him with dark side techniques.
Apparently. Star Wars: Revelations #1 by Marc Guggenheim and a selection of illustrators shows the galaxy didn't need the Jedi to destroy Palpatine.