I disagree with your last paragraph only.
Personally, I don’t think the State has the right to kill other than to prevent others dying (eg armed Bobby shooting a gunman) or, in war, killing such of the enemy as will bring the end of hostilities about.
Your arguments about the practicalities- inadequate legal system, from Plod to Screw to parole service- I’m with you entirely.
I’m just not of the view that anyone, least of all some Civil Servant, has the right to kill, in cold blood, someone who is not a threat to anyone. Whatever they’ve done.
Edit: except Piers Morgan, obvs. Hang him.
The state, in principle, is merely the amalgam of the views of the people.
Society accepts killing for political ends. Basically, the state/society says when it's ok to kill. Different people have different red lines, different rules about when it's ok.
Imagine a very small society, where government amounts to everybody having a say. Society's rule, the law, is a decision of the whole tribe and I suggest they have a right to kill those they see as a threat. Their judicial killing is societal self-defence.
Our society is a lot bigger, and governance therefore different but any sanction/punishment/revenge is still, in principle, our means of self-defence.
However, regardless of all that bilge, I accept that your alternate view is at least as valid as mine.