It's not like we're killing everyone who's accused -- we're killing people that were convicted so positively by a court of law that the judge felt that the correct penalty for this human being is death. Obviously there'd be some people who slipped through the cracks and would get killed, but that's a small price to pay in comparison to the weight on society caused by keeping people ineligible for reentry into society in a cell.
The cost of possibly executing an innocent human generally outweighs the cost of possibly sparing a criminal. It's the reason why Blackstone's Formulation is so popular, and why the vast majority of democratic nations have abolished the death penalty (with the exception of the United States, but the US has a habit of breaking all of our nice trends).
I'm not saying it's an objective truth, but it's how most people view it (who live outside of the United States, and in countries not controlled by Sharia Law or authoritarian Communists).