Would you use teleporter technology if it existed? Why or Why not?
You know those sci-fi teleporters like in Star Trek where you disappear from one location then instantaneously reappear in another location? Do you trust that they are safe to use?
Oh, hell yeah. Plus it's canon that it can heal some diseases.
Now, WRT the continuity of consciousness... hell, I lose that every night, and whenever I get major surgery. Heck, I've transported innumerable times if teleporting a break in continuity of thought plus a change in location. I passed out once from heat stroke and woke up in an infirmary.
Do you consider your brain going in to sleep mode, providing you with filler content that you largely forget, and then waking you back again later to be the same as being vaporised in your original location?
... and recreated, at the atomic level somewhere else? Yes.
Full-body anaethesia is a better example. It isn't sleep; your body is essentially dead, and machines are performing your normally autonomous functions for you.
They both involve a state of unconsciousness, but they are fundamentally different states. If you were under anaesthetic and, whilst under, they liquidised your brain and installed an exact copy of it in its place then you'd be cool with that?
No one would be the wiser and the original brain is gone, so no harm, no foul?
I think I would be OK with it. I'm not the same person when I wake up in the morning as when I went to sleep as it is; my brain is certainly different than it was last week, much less dozen years ago.