The galactic empire was feared by many, but Emperor Palpatine designed it with a huge flaw - one that guaranteed its destruction in the Star Wars saga.
After ascending from his role as Chancellor to Emperor, Palpatine initiated Order 66. The clone troopers turned on the Jedi, and it was a slaughter across the galaxy. Very few Jedi survived, and those who did had to scramble into hiding. This was when Anakin Skywalker transformed into Darth Vader and became obsessed with finding his old master Obi-Wan Kenobi. He was so obsessed that Palpatine had to order him to give up his quest for revenge on one individual and focus on eliminating the Jedi Order as a whole.
In Star Wars: Purge - Seconds to Die by John Ostrander and Jim Hall - part of the Star Wars Legends continuity - a band of surviving Jedi were able to use Darth Vader's obsession with finding Obi-Wan Kenobi against him. They had rallied in the spice mines on Kessel and set a trap by letting it slip out through the Empire spy network that Obi-Wan was hiding there. Of course, Obi-Wan was on Tatooine, but Vader couldn't pass up the opportunity to try and take out his old master. Eliminating the Sith Lords was a top priority for these Jedi as they speculated that Palpatine was a Sith Lord himself and eliminating him would essentially cause the entire Empire to crumble.
The Empire Couldn't Survive Without Palpatine
Even though this was just speculation about Palpatine single-handedly holding the Empire together, it was undoubtedly correct. During Return of the Jedi, once Emperor Palpatine was betrayed and killed by Darth Vader, the Empire folded all but immediately. There were lingering threats that still had to be dealt with as seen in The Mandalorian, but for the most part, everyone in the Empire had to do the bidding of the man at the top. It was built completely on faith of his authority. Without it, the Empire just couldn't function. Indeed, Palpatine actually designed the Empire to collapse in his absence. In modern Star Wars continuity, this was because he had secondary plans to survive on Exegol, and didn't want his former organization providing any competition.
Palpatine's quest for power was never about ideology or sincere belief, but rather about his own supremacy. His greed and narcissism were so extreme that not only could he not imagine the Empire surviving without him, but he specifically didn't want it to. Sith are selfish by nature, believing only in the physical world, not any conceptual ideas of legacy or influence. The Jedi guessed right when they theorized that ending Palpatine would be enough to bring the Empire tumbling down, but sadly their tactics weren't enough to actually defeat Star Wars' ultra-powerful Sith Lord.