The idea that the punishment should fit the crime has a long history and is one of the most basic tenets of justice. To quote Immanuel Kant:
if an offender "has committed murder, he must die. In this case, no possible substitute can satisfy justice. For there is no parallel between death and even the most miserable life, so that there is no equality of crime and retribution unless the perpetrator is judicially put to death (at all events without any maltreatment which might make humanity an object of horror in the person of the sufferer)" (Kant 1887, p. 155).
That's true, but the idea that because some escape justice all should escape justice isn't very convincing.
Of course I would strongly protest the injustice of my particular case; but I doubt it would change my support for the death penalty. Of course, it's pretty hard to say how one would feel in such a circumstance. But I can also tell you I"d not be too happy being wrongly imprisoned either.
But before you say, "but they can correct a mistaken imprisonment"; I say a wrongful death sentence can and often is overturned. It's not like we execute people the day they're convicted. There's plenty of time to correct errors, and I suspect that more resources are devoted to defending guys on death row by anti-death penalty groups than to random guys sentenced to life in prison. So your chances of having a wrongful conviction overturned when sentenced to death may be better than when sentenced to life.