So murder is conservative?
There are well known capital crimes. No one forced anyone to commit them, but by any measure some crimes are so horrible, so contrary to human nature, that those crimes are cause to keep those who commit them from ever reentering the rest of humanity.
These are not the insane, nor those who can plead temporary insanity under the influence, but those who calmly and with forethought and malice commit heinous crimes, including "crimes against humanity".
While we need ever be careful that no innocent person is convicted, that is a matter of cleaning up the courts and those who prosecute cases (and bring them).
These are often unrepentant, admitted killers who have been confronted with physical evidence of their crimes, who have shown knowledge of those crimes which would only be known to the killer, given locations of bodies, etc. These are not innocent people.
Their death, and in this we especially digress, for I would have it public, and brutal enough to dissuade others, could serve as a deterrent to others who might consider committing similar crimes.
For what cause would you preserve them in a prison population where there are those who might be inspired by them to follow in their footsteps?
Would you say the hangings after Nuremberg were murder, too? After Lincoln's assassination?
If not, where do you place the cutoff?