EVERYBODY on death row is there because they have been found guilty beyond a reasonable doubt.
It just so happens that “without a reasonable doubt that they did the deed” does not in fact mean they did the deed, because the American criminal justice system has a number of serious flaws.
Well, that’s rather fighting the question, though. There are instances of murder where it is full-out obvious who the murderer is. Take Jack Ruby, for instance - shot someone dead on live TV in front of millions. Do you think his guilt was seriously in question?
It’s great that someone with no claimed legal or corrections experience understands the system well enough to fix it, but have you considered that it might be more complicated than you realize?
Was Jack Ruby legally sane at the time and did he possess sufficient mens rea to support conviction? (Texas, then and now, recognizes insanity as a possible defense, and in fact that WAS the basis of Ruby’s defense; his lawyers argued that he had both personal and familial history of mental illness.) What full-out obvious and unimpeachable evidence would you present to prove his sanity?
There are other possible arguments where a person committed the deed but is not guilty of the crime: self defense, for example, or compulsion.
As it happens, Jack Ruby’s initial conviction was overturned on appeal: the Texas Court of Criminal Appeals unanimously ruled that he could not have received a fair trial and proper consideration of his defense in the highly-charged atmosphere of Dallas, and they remanded the case for a change of venue. Ruby died before that second trial took place.
I would also presume they are lower priority. You’ve got 'em locked up, so there’s no real reason to rush. There’s not much lost in letting them take their time. At the very least, appeals cases in situations with people not in jail would take priority.
I also note that states have also had difficulty actually doing the killing, since lethal injection requires medical training to do correctly and a pharmacy willing to make the drugs, with both tending to put saving lives above causing death. There are even reports of a state hiding why they want to buy the drugs because the sellers wouldn’t sell it to them if they knew. And even if you are willing to do it, ending someone’s life does not tend to be something you are eager to do unless it’s personal.
But, yeah, it’s mostly just giving time for the process to complete to avoid any chance that they would be exonerated, and because it’s in the best interested of the convicted to draw it out.
As the sole survivor of the Connecticut home invasion Dr. William Petit, who lost his wife and daughters to two men who broke into their house, tortured them and then set the house on fire, said “Do you want a criminal justice system based on economics?”
The two men who did this agreed to plead guilty in exchange for life in prison. The prosecutor did not agree, and went to trial.
The murderers of William Petit’s wife and two daughters aren’t on death row any longer. The state supreme court declared capital punishment inconsistent with the state constitution and commuted the sentences to life without parole.
If you are on death row and there is evidence that you may not be guilty there are groups that will help you for free. If you get life there is less help available.
With enough long-term semi-solitary confinement, there’s always the chance the prisoner will go nuts, and then his supporters can argue that the state mustn’t execute an insane prisoner.