This "debate" has been over in all other nations that the US likes to be compared for years.
It is similar to the "tough on crime" incarceration "debate" in the US, where perverse incentives and political expediency has led to the US being the highest-per-capita incarcerator in the world.
Framing the death penalty debate around "innocent people get killed" will not change the partisan/class perceptions.
The US criminal justice system requires root-and-branch reform, starting with issues around policing, cash bail, school-to-prison pipelines, and unfair drug and "victimless" crimes.
Australia has been going through a similar debate and is at a similar point, without the death penalty, but dealing with the systemic racism and other class related issues.