So trial and conviction by one or more juries, endless appeals and an average stay on death row of over 20 years before the sentence is carried out compared to walking into a convenience store and blowing away a clerk is not a higher standard?
In what universe?
Higher? Certainly. High enough? Debatable. I've seen enough coerced confessions, stacked juries, railroad jobs and outright bigotry under color of law that I'm loath to entrust the state with the power to determine life and death. That's even before DNA testing, which offered the first definitive and scientific proof that things are not what the jury thought they were.
(As an aside, DNA testing does not "prove innocence" -- a victim could have been raped by one person and murdered by another. Unlikely, but possible. A negative DNA match does undercut the case for guilt and raise a large, never mind reasonable, doubt.)