Context is a thing.
Concerns about what amounts to about one death a decade is frivolous when compared to more like one hundred per day.....
This is a terrible argument. How can we be upset about Ukraine when many more people are dying in multiple African wars? How can we worry about all those hundreds of deaths you are talking about when COVID is killing so many people in jails?
Newsflash: People can chew gum and walk at the same time.
I wonder if instead of spending all that money on appeals, if it wouldn't be cheaper to just retry the defendant?
It would be better to assure people in criminal cases got effective counsel in the first place. Half the cases (or more) of the wrongly convicted I hear about had defense attorneys who were grossly incompetent.
And more than a few prosecutors need to be fired when they are found to have concealed exculpatory evidence. There needs to be more motivation for these jerks to stop doing that.
Re the rest of your post, the limitation on appeals is an issue. I can see the problem if defendants get unlimited appeals. OTOH there needs to be some kind of neutral evaluation of that exculpatory evidence.
And from what we know about eyewitness testimony being unreliable, no death penalty case should be based on eyewitness testimony if there is no corroborating physical evidence.
And the forensic lab people need regular random confirmation testing of their findings. It would find falsified results but it could also put a check on bad science like bite-marks and arson evidence. Once these kinds of errors are found it should lead to major reforms in forensics, and to some people being fired and/or prosecuted if it was willful.
See the John Oliver piece. Police battering to get a confession really needs to stop. There's a woman scheduled to be executed next month who was battered into confessing she killed her baby through abuse despite the fact the police video is available and they clearly battered her (verbally) until she confessed. And again there was exculpatory evidence which wasn't presented like her other kids saying she never abused any of them. We know this kind of police interrogation gets false confessions on a regular basis.
I might have posted this before, it's a long thread: SCOTUS Scalia once said in an interview he was fine with an innocent person being executed as long as that person had due process. How disgusting is that? Instead of saying the 'process' needed to be reevaluated, he just sat there all smugly saying he wouldn't lose sleep over state sponsored murder.