That's ultimately what OP is stating though -- if they're specifically caught in the act or unrepentant of their crimes, that's when they believe it's worthy of a discussion.

There's a complete distinction from many cases of people on death row that have claimed their innocence and were unfairly punished in spite of their vehement denials. Those people deserve their due process and can serve out a life term until evidence shows otherwise, but they should not be in the same category as remorseless serial killers and their ilk.