I don't think I agree with your statement, however. It IS terrible to execute an innocent person. However, you're assuming that bad outweighs whatever good may be done by executing the guilty. Whether there IS any good done is arguable, but until you determine that, you're saying "Pros - Cons < 0" without knowing the value of the pros.
The fact that prisoners maintain their innocence is really not surprising. I think this is a basic fact about human nature: we are frequently dishonest, especially when trying to maintain a positive view of ourselves. This quote from "How To Win Friends and Influence People" gives a striking example to make that point:
<quote> When Crowley was captured, Police Commissioner E. P. Mulrooney declared that the two-gun desperado was one of the most dangerous criminals ever encountered in the history of New York. "He will kill," said the Commissioner, "at the drop of a feather."
But how did "Two Gun" Crowley regard himself? We know, because while the police were firing into his apartment, he wrote a letter addressed "To whom it may concern." And, as he wrote, the blood flowing from his wounds left a crimson trail on the paper. In his letter Crowley said: "Under my coat is a weary heart, but a kind one -- one that would do nobody any harm."
A short time before this, Crowley had been having a necking party with his girl friend on a country road out on Long Island. Suddenly a policeman walked up to the car and said: "Let me see your license."
Without saying a word, Crowley drew his gun and cut the policeman down with a shower of lead. As the dying officer fell, Crowley leaped out of the car, grabbed the officer's revolver, and fired another bullet into the prostrate body. And that was the killer who said: "Under my coat is a weary heart, but a kind one -- one that would do nobody any harm." </quote>