Your problem is drawing up a set of rules that would qualify someone for execution.
Heinnous murder, easy enough, but a lifetime criminal, perhaps with a string of burglary convictions, how many convictions is enough ? 10, 20, what about equating that to say a few street robberies, and how many of those equals one rape ?
Do we point score offences, hit a certain number and you’re out ?
It’s easy enough for me to see which ones will never make the grade, but how do you control what is effectively my opinion ?
In principle there might be an argument for getting rid of such wastrels, but enacting it would mean long appeals procedures, there would be strange anomalies as politicans of the day recategorised offences according to public mood, we have seen this with the three strikes rule where one offender got a life sentence for stealing a piece of pizza.
Even those on the side of the angels have many flaws and will get it seriously wrong, this is why in the US the appeals procedure for capital offences is supposed to be very thorough.
I personally would not have too much difficulty in selecting and executing certain criminals, those who you would categorise as lifetime drains on society, but that should disturb you, think of how easy it would be for someone like me to get too adventurous, and think about what society would be like if folk like me could be let loose with judicial killing.
Just give me the gun and the warrant and maybe a mop.
Do you think that the criminal justice system is a good one if it could create folk like me, who could kill so casually ? It would also be a reflection on the rest of society too, including yourself, you would be giving me your permission to select and kill multiple serial petty offenders.
Be careful what you wish for.