I think you are giving the death penalty too much benefit of the doubt. The US has removed hundreds of people from death row, mainly because the ability to study DNA evidence has improved. The technological shortcomings of a single field nearly sent well over a hundred innocent people to their death. This is just old cases that still had useful DNA evidence, haven't carried out the execution yet, managed to be successfully reopened and ended up getting overturned. Some cases are affected by prosecutorial misconduct, others by
sloppy employees or lazy investigators, and often you have juries that are stuck with only one suspect and feel like they have no other explanation. There are many ways that an innocent person could be found guilty, and I think it happens more often than people should be comfortable with.
You've brushed off significant costs without addressing whether the benefits outweigh them. It hasn't been shown to be effective in deterring crimes or improving the lives of victim's families, since the trails tend to drag on much longer if the fate of someone's life is being decided. The legal costs are much higher when the death penalty is pursued, which is warranted since legal fees should not be a determining factor in the outcome. What benefit does it have, aside from satisfying bloodlust? I'm not "soft on crime" and I think punishment and rehabilitation should both be a significant part of the sentence, but why is there a systematic need to make them pay a price that you could never refund? Can you actually show significant benefits to that, outweighing the costs, that can't be achieved with life behind bars?