I’ve seen the evidence, in fact I’ve had my nose rubbed in it. But, conjecture and anecdotal stories are not really evidence. Certainly we must be especially certain of a criminal’s guilt before we put them to death. We should always look at all the evidence available and be willing set aside the death penalty if there is not overwhelming evidence of guilt. On the other hand, appeals that do not go to guilt but rather to procedure should be strictly limited and sentences carried out expeditiously. There is no legitimate reason for criminals to live on death row for generations.
Will mistakes be made? Almost certainly! Nothing done by man is perfect, but the system is now such that it will certainly be extremely rare. Over the years I had several friends and acquaintances killed in aircraft or vehicular accidents. We don’t stop flying, driving or riding because of the miniscule possibility that each time we do so may be our last. Similarly, people have spent a lifetime behind bars for crimes they did not commit. Certainly no less an injustice that being put to death. That does not mean we quit locking people away.
As for the families of people wrongly convicted and put to death, I don’t think you’ll find many. But if you do, they will at least have a cause of action and recourse to meaningful redress. Not something that can be said for the families of thousands of murder victims each year.
Some have said that the measure of a society is how it treats its criminals. I disagree, the true measure is how the victims and their families are treated and whether or not justice is done.