I think the primary environment around the avoidance of “cruel and unusual” is that the dispenser of the justice remain publicly dispassionate and not get, or appear to get, vicarious pleasure out of it along with the prosecuting staff not being able to get political points for it.
I agree. Right after such a horrendous crime, We The People tend to want a similar horrendous punishment, naturally. We want justice; we want a strong deterrent for future such crimes. We want revenge beyond a measured response. And after decades of such injustices, we want to destroy those we rightly perceive as enemies of human civilization.
So our "civilized" measures of justice are the best we'll ever see from the systems we put in place.
When those systems fail, and cannot provide even a minimal level of justice, we will see vigilante justice, such as is happening in places like Brazil.