A bad sentence against innocent people is an unavoidable circumstance with no end in sight, you're confusing wrongfully found guilty and the method of punishment. A genuinely innocent person will simply not be the man who comes out of a decade in jail if they are found innocent, killing them or leaving them to be brutalised in jail, both are horrifically awful outcomes, neither is better or worse, either way you kill the man that goes into jail, one way the innocent man has some relative peace, the other way another man comes out of jail after years or decades of often horrific treatment a completely different person anyway.
I'd choose to die, innocent and wrongly accused the person I am than a beaten, tortured person 10-20 years later unable to live normally anyway. Get rid of the death penalty in the states, innocent people are just going to end up in gen pop being treated much worse and having their lives completely destroyed, just in a different, much more violent, much worse way. The problem is the legal system and its focus, usually politically motivated, causing one person commiting a crime to get one punishment one month and a different punishment 3 months later when the same crime isn't as "popular" in the media. Likewise prosecutions choose who to prosecute, if in the publics eye someone is SEEN as being guilty and the crime is particular in focus in the media, prosecutions are more likely to push for a conviction on bad evidence than at another time when they might think getting a conviction helps no one.
When people's jobs are based on the publics opinion, and therefore who gets prosecuted and why is subject to people getting elected and looking as tough on a changing scale you're in trouble. None of that has anything to do with the death penalty.