But the argument that it does deter is also weakened. It's unfalsifiable if the response to "we removed the death penalty and crime did not increase" is "maybe

But the argument that it does deter is also weakened. It's unfalsifiable if the response to "we removed the death penalty and crime did not increase" is "maybe crime would have started falling, and removing the death penalty prevented that". (I know that's not what you said, but it's an extension of the argument you describe.)