Let's say we sentence somebody to life without parole, and twenty-five years into his sentence we discover that he's actually innocent. How do we make that up to him? If he was 35 when he went in, he's 60 now. Who will return to him the years that the locust has eaten? Saying, "Oops. We're sorry." doesn't really seem like enough, you know?
For that matter, I remember when Ray Donovan, President Reagan's first Labor Secretary, was smeared by accusations of misconduct in his prior business dealings. He resigned in order to fight the charges, and won. As he stood on the courthouse steps, fully vindicated, he said, "Where do I go to get my reputation back?" He had been dragged through hell, had to resign his office, spent enormous sums of money defending himself, and was assumed by many to be a crook. How do we make that up to him?
The fact of the matter is, almost everyone assumes that the State has the right to deprive us of our liberty and our property with hardly an apology, let alone restitution, if we turn up innocent. And even if we were to be offered compensation, you can't give people back what they missed out on, nor can you erase the awfulnesses they endured, while fighting the charges.
In the case of health care, many death penalty opponents blithely assume that government-mandated health care rationing is more fair than rationing by deep pockets or private insurance. That may be so, but the assumption remains that someone, somewhere can tell you that you can't have that fancy new drug, and that can be as much a death sentence as any imposed by a judge and jury.
While we're on the subject, the Supreme Court has noted that "the power to tax is the power to destroy." Nobody is saying the gummint can't lay and collect taxes, even if they bankrupt you and put you in hock to the IRS forever.
The problem isn't the death penalty. The problem is State power. And, as one of the founders (Madison? Adams?) long ago said, "Government, like clothes, is a badge of lost innocence." We can't avoid State power. So, will we hold government accountable and try to make it work right? Or will we allow it to abuse people in all kinds of ways, including ordering their deaths, so long as they don't die at the hands of the State because of a crime they committed?