This issue of appropriateness was the whole reason that Hammurabi carved his stele and set them up throughout Babylonia.Is execution the "appropriate manner" of punishment that you'd stipulate for all crimes that "cast doubt on whether the offender should be allowed" to exercise their 2nd Amendment right?
Appropriateness is measured by the offense.
Hammurabi said "no more than an eye for an eye" in other words don't execute someone for a mayhem incident.
While Moses excused accidental manslaughters, murder has always carried a sentence of capital punishment with it.
The Chinese are even smarter than anyone else -- they harvest organs from murderers so that other patients' lives can be extended at the expense of the execution of the murderer who obviously took a life illegally and cannot restore it but can restore life to others. Of course in some cases like AIDS or hepatitis the organs are useless even then.
It would be creepy going into surgery knowing you were not going to ever awake from it again, but the price to be paid for murdering someone should be high. Otherwise everyone would be doing it.