It is true that executions by the state are not typically viewed by average people but the average person has probably been exposed to the way we execute people in one form or another. It could be through a re-enactment, a dramatization, a recounting, archived footage from a documentary, or some other such method. The idea that lethal injection is a humane method of punishment is much easier to sell than depicting a row of rifleman shooting someone full of holes. For example, until France abolished their death penalty their method of execution was guillotine within the walls of the prison. The idea of the state beheading people was too much for the sensibilities of France in the 70s even if they didn't have to watch it happen. Beheading in this manner may also ultimately cause less panic and pain to an unwilling participant than a nitrogen chamber might but the idea of it is much more horrible.

My underlying point of course being that there isn't really a humane way to kill someone or even a relatively humane way aside from deliberate torture. The idea that there might be I think allows the practice to continue by making it easier to tolerate even though it probably shouldn't be. This is aside from the larger problems of it being completely permanent and therefore with zero tolerance for error or bias at best and legitimizing the idea that a state may legally kill its own citizens under some circumstances at worst. The case in this article is far from clear with the judge overruling their jury to impose a death sentence when the jury didn't believe it was merited in this case. A judge being this cavalier about peoples' lives being the final say in the matter to me indicates that the death penalty is not being taken as seriously as it should.