After Shmi dies, Anakin is understandably upset and frustrated, and he tells Padme he will one day become so powerful, he will even be able to stop those he loves from dying. He then has visions of Padme dying. This is another event Palpatine uses to manipulate Anakin, but I don’t think his offer is entirely empty. There is a glint in Palpatine’s eye as he mentions how Plagueis could save others from dying, but not himself. I think Palpatine returning fits right in with his quote about the the Dark Side being a pathway to abilities some consider to be unnatural.
On a side note, when trying to speak with Vader, Kylo says he will finish what Anakin started. I don’t think he had this in mind, but in a way he was able to do what his grandfather couldn’t. He did save the one he loved from dying.