It wouldn't be a solution for a personal existential dread of death. It would be a solution if you were trying to uphold long term goals like "ensure that my child is loved and cared for" or "complete this line of scientific research that I started." For those cases, a duplicate of you that has your appearance, thoughts, legal standing, and memories would be fine.
I cannot be 100% certain that sleep is not fatal. If I had some safe and reliable means of preventing sleep I would take it without hesitation. But it seems plausible that a person could survive sleep because it's a gradual process and one that everybody has a lot of practice doing. However, there are no such mitigating factors with general anesthetics. I will refuse general anesthetics if I am ever in a situation to do so. I believe a combination of muscle relaxants and opioids can serve the same medical purpose, which I do not believe would kill the person.