I think people are get very muddled when they attempt to put their positions into words. That doesn't necessarily mean they're being deceptive. Sometimes it's just a skill issue. I think that what I have described is the "coherent" version of the position (the steelman, if you like). I like to lay it out like that because it makes the discussion about the thing it is actually about, which is, as you said, whether a right to vengeance makes sense or is something we want to enshrine in our society.

Now that I'm thinking about it there is at least one other coherent position I know of for it, which is: if you start out thinking of life as rather 'disposable' (so humans are somewhat equivalent to animals, which we regularly raise to eat; war is okay; things like that), then the argument for keeping people alive is that they contribute to society or at least don't heavily detract from it, and the argument for putting them to death is that people have proven themselves not even worth keeping alive. This opens a whole different can of worms though where you have to explain where your bar for keeping people alive is. but I do think it is ultimately how a lot of people think about it, as well---at least in regard to people who are not part their personal community.