I agree with everything you've said, but the policy for this needs to be thought out very carefully.
Because of suicide contagion, it's not exactly analogous to discussion of limb amputations. Even though discussion of assisted dying/euthanasia isn't the same thing as discussion of specific suicides (as per suicide contagion), the policy still needs to be well considered.
Euthanasia is killing somebody out of "mercy." It does not require the agreement or desire of the person being killed.
It is definitely a step beyond physician-assisted suicide, and the two should not be confused or used interchangeably, though both are morally repugnant.
Either your country is handling assisted suicides in a terrible way, or you don't really know what you're talking about, as rude as that makes me sound.
Especially "It does not require the agreement or desire of the person being killed" is absolutely, 100% false.
I'm not talking about laws. I'm talking about the meaning of words. What is it called if a doctor kills somebody out of "mercy," but without explicit consent? An increasing morphine drip that suppresses vital function allowing them to "go peacefully in their sleep" just a bit sooner than would have happened otherwise. This happens all the time.
That's called euthanasia, not physician-assisted suicide. And if we can't acknowledge the difference, we are opening ourselves up to allowing what I described because we already allowed "euthanasia," when in fact what we really allowed was PA-suicide. The fact that both are murder in a moral sense doesn't change the necessity of distinguishing between them.
It could be argued that performing a surgical procedure is harm - after all it destroys various tissues using a knife.
But there’s a difference, and it’s the same difference as between euthanasia and suicide.