There are several problems with this but I'll touch on two:
1. Other than some primitive revenge fulfillment, how would that be in any way a better solution for society at large than locking you up until you die?
Well, revenge is a motivator enough for many people but I agree it's insufficient and shouldn't ever be used as justification for a particular punishment.
For the most dangerous criminals guilty of the worst classes of crime, removal from society is the best thing. You have two choices for that: death penalty or life imprisonment.
The problem with the latter is that eventually you reach saturation; there simply isn't room to house criminals. Consequently, very few people are imprisoned for "life". You can't rely on imprisonment as a punishment for all serious crimes and if you did, what would you do for all the lesser crimes where imprisonment for a period of time would be the best punishment?
When convicted murderers/paedophiles etc walk free from prison only to commit whatever crime they were imprisoned for again, what are you going to do?
I do think that there are some crimes for which the death penalty ought to be considered as an option, but it would have to rely on the soundest possible conviction.
2. How, if you wish to implement the death penalty, do you ensure that no one is ever wrongly convicted?
You can't. No system of justice is perfect.
However, suppose you implemented true life imprisonment. If you lock up an innocent man for his entire life until he dies, other than the time taken for his death, how is it different?
I don't think telling ourselves "well, at least we never killed the poor bugger" is going to appease our conscience over the fact his life was effectively taken from him.