What do you mean, "We haven't found that person yet"? There have been 17 people EXONERATED by DNA. Many more were AQUITTED at re-trial.
Innocence: List of Those Freed From Death Row | Death Penalty Information Center
As for, "I guess the reason I don't lose a lot of sleep over the issue is that the kinds of people who get "wrongly convicted" usually did a bunch of bad stuff that they were never caught doing." That is just plain wrong no matter how you slice it.
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What you haven't found is a wrongly executed person. You've found people who got death penalties, didn't actually commit the crimes they were convicted of, but committed plenty of others.
You look at your "exonerated" criminals, you get clowns like Rolando Cruz. Been in trouble with the law before, have been in trouble since.