I didn't see you referring to the legal process beyond simplifying it down to 'depends on the evidence' and 'suitable evidence'. Evidence is not simple. For example, eye witness evidence is one of the more common forms of evidence seen in convictions, yet by far the most common in overturned convictions. While DNA or other forms of physical evidence may place a person at a scene, or in prior contact with a victim, it doesn't necessarily mean they are guilty of the crime, yet people are convicted on this kind of evidence.

I don't think we're anywhere near being confident in establishing conclusive guilt that'd justify the state killing someone. The idea that somebody's life would hang on an adversarial system of justice, where the state's role is to secure a conviction, doesn't make much sense. Perhaps it'd begin to make more sense where the prosecution is replaced by a role whose purpose is to find the truth one way or the other?