Getting back to executions.
On a curve of suffering, take the central majority, that within a standard deviation on a rating of suffering.
If the same suffering were inflicted by prison authorities, how many patients' deaths would violate the Eighth Amendment prohibition of cruel and unusual punishment?
The original intent was to prevent outright torture, suffered at the hands of the British. If done to a person by another, how many deaths would qualify as torture?
The death penalty was deemed that in the 1970's and banned because of bias against minorities. Not because of its manner of death. As these inequities were removed by the states, the death penalty was permitted again.
As a soft guide to a definition, any procedure that "shocks the conscience" may be cruel and unusual.
Suffering in death seems universal, and not unusual. The average person's death is quite cruel, and if inflicted intentionally by another would shock my conscience.
If the average person has benefit of medical care at the time of death, does depriving the condemned of medically trained executioners, and medical supervision, does the deprivation violate the Eighth Amendment, and the Equal Protection clauses of the Fifth and Fourteenth Amendments?
And the AMA prohibition of medical participation violates those.