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human
[Star Wars] Why did Palpatine rescue Vader on Mustafar?

I suppose the greater question I'm asking is why did Palpatine feel the need to continue the Sith tradition of keeping an apprentice after toppling the Republic? He knows first hand that people become the Sith Master by overthrowing their master, and he was someone that had overthrown the Republic, implanted himself as the ruler, and more than any other sith master, had the intention and means of living and ruling forever, why would he keep the one tradition most likely to spell his doom? I understand that the idea behind the master and apprentice scheme was because it was usually those two against the entire galaxy, and Palpatine used that principle effectively with Maul, Tyranus, and Vader until the fight on Mustafar, but after that he would presumably have no need of an apprentice after that, and little would have changed. I suppose maybe Palpatine wouldn't want to have to run the Inquisition himself, but that is the biggest change I can see.

Especially considering that Vader getting critically wounded on Mustafar granted a unique opportunity to Palpatine. If there was ever a Force user that could overpower Palpatine, it was Anakin, which is why Palpatine sought to turn him. With Anakin being critically wounded however, Palpatine could have just left him to die and rid himself of the one person in the galaxy that could ever threaten him.
gpt
He wanted Vader because he was useful. The rule of two is that there is a Master with the power and an apprentice to desire it.

While it is true that Palpatine has mixed feelings about this across continuties as he does not desire to truly be overthrown, this does not mean he does not recognize how useful it is to have an underlying


The damage done to Anakin on Mustafar was a blessing in disguise because he lost a lot of midichlorians and as such his connection to the force was diminished. He may've had a chance of surpassing Sidious originally but with the chance brought down, he now had a perfect pawn. Who had nothing left in the galaxy but him.

On top of that, at least in Legends lore he made Vader's suit vulnerable to Sith lightning so he could never truly face him and on top of that he also intentionally didn't teach him everything. Which he is probably doing in canon. You don't teach them everything so they cannot surpass you. Sidious is still a Sith, so he is arrogant. But even with that arrogance he actually has a solid system for keeping Vader in check. And for the most part it did work.

And this is to say nothing of his clone plans or how apparently Sith possess the body of their successors. So even if Vader did kill him, he would just become him and truly carry on the way of the Sith.