Well, if having the death penalty didn’t reduce crime genetically, removing it wouldn’t increase it. However, it would be difficult to remove the social and economic noise to find a genetic signal, even if there was one. If parents felt they had to steal bread for their children, I’d think providing them bread would cut down the crime rate far more effectively than executing the ones who got caught.
That’s still only a dozen or so generations. Not nearly enough time for natural selection to work its magic.
Selection only works if there is a mechanism that actually efficiently selects. The death penalty both now and in years past was so arbitrarily applied that it amounted to little more than bad luck. The reason eugenics would never work, because fallible humans would be trying to impose it.
Cite?
No specific cite to offer, only the common-sense observation that the poor and low status were and are far more likely to be executed than the rich and powerful.
That is effective selection if you assume the poor are more likely to have inferior and/or criminal genes, which many do assume.
Are you allowing for the fact that the former way outnumber the latter?