Imagine you have a device that transmits your brain signals into another body so that you can control 2 bodies at once. Clearly you are one self that is controlling two bodies. Clearly destroying either one of these bodies wouldn't really kill you (so long as your brain is fine) you'd just continue existing in the other body.

Now let's say we copy your brain exactly and put it in the other body, and then a device that synchronizes your memories and experiences. body 1 would act exactly like body 2 in every circumstance. I don't see the difference between the first scenario and the second, you are one self, distributed across 2 brains and 2 bodies. If you killed one of the bodies, no one would die, it would be more akin to losing a limb.

Now let's remove the synchronizer, for the first instant it's identical to scenario 2, but over time the 2 selves would diverge and become separate people.

so as long as we kill off the old self immediately before or at the same time as the new body comes online then I don't see it as a murder machine like you describe.

however, if we have the tech to copy the body perfectly, who is to say we can't improve the body as teleport them, make the new body stronger or disease proof. And if we do that, who's to say we couldn't make small changes to the thoughts or memories, make you more docile or forget injustices. That seems pretty risky to me.