Nor the imagination to connect their signature on a death warrant form with the demise of an actual human being.
Well in a sense you may be right.
Usually the mind set of these people (the true believers) is that they dehumanized the victims in their minds as vermin not deserving of life.
Some of them are merely government workers who decide it is either the victim or themselves and their families. They do the math in their head and decide that their lives are worth more. They know that they are sending someone to their death but do not have the courage to say no.