I can understand the practical reasoning in regards to rape, but as I said, it's a bitter pill to swallow. You're essentially compromising with rapists, in order to reduce the rate at which they murder as well.
Personally, I agree with you on point (i), but disagree on all other points. Miscarriages of justice would probably kill fewer people than dogs do every year, it only leads to higher costs if you allow appeals to drag on for years, and killing people is something that both soldiers, and those who perform assisted suicide, do all the time. It'd probably have higher job satisfaction and be less traumatising than working in a job where you had to kill (innocent, healthy) animals constantly.
Revenge? Possibly sometimes, but it's also just about getting rid of people who have proven themselves to be an incredibly harmful, net negative to society, rather than keeping them alive for no real reason whatsoever. I don't see any moral reason to keep a sadistic paedophile alive for 30+ years in prison, for instance. It's arguably more moral, imo, to just cleanly kill a person who is not suitable to be in society, and go on with life, rather than keeping them in a box until they die.
In the past we would've probably just exiled people, evicting them from the tribe, which was most likely a near certain death sentence - but unfortunately that's not an option anymore.