Taking the life of the murderer does not return the victim to his or her loved ones.
State-run executions are political theater to terrorize the population to behave better, using the ancient "eye for an eye, tooth for a tooth" concept as the underpinning of their moral authority.
This is vengeance or wrath, one of the so-called Seven Deadly Sins.
But innocent people have been executed because of kangaroo courts, race-based misidentification, or the need for vengeance.
The Innocence Project has exonerated hundreds of death row inmates who were falsely convicted, an issue that affects poor people, not the wealthy elites.
Moreover, once the murderer has been executed, criminal investigators lose a vital source of information for other crimes the perpetrator may have committed.
Sidenote: The British aristocracy were appalled at the decapitations of French noblemen during the Reign of Terror (~est 17,000) following the French Revolution. But 57,000 executions occured under King Henry VIII's Reign of Terror. William Shakespeare lived at a time (the Elizabethan Age) when just one state executioner himself was responsible for an estimated 3,000 decapitations. That gruesome terminator was a man named Thomas Derrick.
And how many other executioners were employed under Queen Elizabeth I throughout England, Scotland, and Wales?
"Gentle Will" was appalled by state-run violence and war and cleverly steered clear of offending Elizabeth I and her Privy Council, even while cleverly barbing her in some of his plays.
Below, Mary, Queen of Scots, at her brutal and unnecessary execution (8 February 1587):
Hahahaha keep dreaming