A well reasoned argument. Thank you. I have some counterarguments but there is a lot of historical precedent to back up the central objection - monomachy became corrupted by aristocrats hiring bravos which effectively gave the moneyed class an upper hand, and corrupted by lower-classes seeking financial gain by challenging nobles who might not have the opportunity or resources to hire a skilled bravo to fight in their stead.
What about execution by torture !?! Sure mistakes might be made but in the long run, maybe lives would be saved since even psychopaths or frenzied drug addicts might retain enough sensibility to be deterred by the prospect.
If that end was to be a deterrent, the focus would be on those who could be deterred. Not so much psychopaths, serial killers, frenzied drug addicts who are beyond the reach of reason, possibly well before their crimes are committed, but those who could reason, who would decide that the crime wasn't worth the risk of the punishment.
So the sort of crimes to deter would be ones committed by sane people with a clear head, at least clear enough to be deterred by possible consequences. Crimes of passion, of someone on bath salts, committed out of a deep, personal need that had endured and grown since adolescence or earlier (as with many serial killers), wouldn't be the sort of thing a society could deter--either the perpetrator is mentally ill or they are not in a rational state of mind, whether that is due to hatred, anger, insanity, or chemicals.
Most often, kings of old would use creatively cruel means of execution to intimidate the masses, but for lesser crimes (ones we might not consider capital offenses) and for (especially) treason.
There are dozens of 'Boot Hills" out this way with epitaphs reading "hanged by mistake" or some such. Bad enough to imprison the innocent, worse to execute them (can't be compensated in any way), but the thought of torturing the innocent to death?
No thanks.
Standards which should preclude the conviction of the innocent would have to be strictly enforced, and only on the basis of solid physical evidence should any conviction be considered for capital punishment in the first place. Unfortunately, people have been imprisoned on the basis of 'ginned up' evidence, the suppression of Brady Material, and the misstatements or knowingly false statements of witnesses. There is often incredible pressure to apprehend and convict someone, (anyone!), for heinous crimes, brought to bear by the press and the public who just want to feel safe.
Those arrests may be nothing more than a matter of rounding up some (pardon the expression) half-wit or one of the 'usual suspects' to take the fall for the benefit of a beleaguered police department and/or political leadership who is having trouble solving a crime or a string of crimes.
It is not inconceivable that the same sort of situation could be used to suppress political dissent. Once the door is opened, there is no telling how far, nor what will come through.
When I hunt, I dispatch the animal as humanely as possible, quickly to prevent suffering.
IMHO, capital punishment should be done similarly, but in the public eye, with full disclosure of the crime it is being administered for. That deer doesn't get a slug of 'feelgood juice' before I harvest it, the capital offender should not either. Suffering should be limited to that incidental to the anticipation of and the imposition of their fate, not imposed as a means of 'getting even' for the crimes they committed, or even as a deterrent to others, as tempting as that may be.
