And also that the reason for the demographic spread is that this is the demographic spread of the community you are talking about.
I think that you misunderstand. There are very, very few (known) black serial killers. The only one in the US that I’m aware of is questionable; Wayne Williams was convicted of the murders of two adults, but there was very little connecting him directly to the other murders that the Atlanta Police Dept. claimed he committed. My argument would be that, outside of serial killers and serial child rapists, use of the death penalty should be very, very rare, given that the risks to society are very low compared to the possibility that they could ever be released or escape. E.g., someone like Ed Kemper is always going to be a danger to society, until he’s dead.