If we're going down that road, you might as well have inmates fight to the death with weapons in a hockey rink on live TV. Or I guess in America's case, in a steel cage or a baseball inspired diamond type of steel cage or some thing. Or maybe on an aircraft carrier.
Well, a fair number of people already compare the U.S. to the Roman Empire in decline. Why not give people bread and circuses and literal gladiator games? Oh, right. Because some of the condemned would be innocent, and then there would be a Russell Crowe-type person who would end up killing the President because the President fancied himself a warrior and wanted to impress his son... (actually that is not remotely how history really happened for that Emperor, which is why I don't really care for
Gladiator).
Canada has had some awful miscarriages of justice: Stephen Truscott, David Milgard, Donald Marshall, Guy-Paul Morin... just to name a few. All were convicted of rape/murder, and all were innocent. Truscott was underage, and originally sentenced to be executed (we still had the death penalty back then). He was 14. But his sentence was commuted to life in prison, and many years later new evidence revealed him to be innocent.
Of course we've also got undeniably guilty wastes of oxygen taking up room in prison when they don't even deserve to keep breathing: Paul Bernardo, Robert Pickton, Luka Magnotta, the Shafia family... and Karla Homolka who did serve 12 years but should have had life. She's free now, but I very much doubt she's at all rehabilitated or even remorseful.
The RCMP have this noble image outside of Canada - the red-uniformed, Stetson-wearing Mounties who are invariably polite, helpful, competent, honorable, and trusted. Well, there are probably some who are like that. But there are a lot of them who are absolute scum who have no problem at all in railroading innocent people into prison, racial profiling, taking the easy way out, beating and torturing prisoners, and generally being clueless idiots.
So thank goodness we don't have the death penalty. Yes, the worst of the worst get to keep breathing. But the flip side is that Truscott, Milgard, etc. are still alive.
There's a novel by Marion Zimmer Bradley (science fiction one, naturally) in which she depicts one of the characters going on a killing spree and being caught. He's undeniably guilty, and that society doesn't have the death penalty. But its take on prison is this: The prisoner has a choice between chemical "rehabilitation" - literally altering the prisoner's mind to eliminate all capability of committing violent acts - then being retrained and put to work doing menial labor for the rest of his/her life.
The alternative is an escape-proof prison of cryogenic freezing that is perpetual. The prisoner doesn't die, and ages so slowly that it essentially makes no difference. If proof of innocence is found later, the prisoner can be released, alive, and allowed to integrate back into society. They could possibly be decades out of step with their former lives, their families could be lost or dead, but they would be alive. Or alternatively, if the prisoner is never found innocent, he/she stays frozen. The system is, of course, set up so the cryogenic units don't lose power or malfunction, and they're absolutely escape-proof. Those in freeze don't have to be fed, they don't get bored or stressed, there's no overcrowding or violence, just basically nonexistence unless they're revived and declared innocent.
So would that be a more humane way to handle those whose crimes might otherwise merit death? The technology to make this work flawlessly is something we don't yet have, and there would need to be a radical change in laws and societal attitudes against human experimentation (since this system would have to be tested on humans to see if they could be revived successfully and those remaining frozen would not age or suffer).