* We want to rehabilitate but we also want to punish.
* We want to be humane but we also want to kill. So we keep switching around our methods until we got to these drug coctails. Which some first paralize the person, so when dosage is off, they could be in a horrible agony, but you know, they are not thrashing around making unpleasant sounds, so the sensibilities of those watching are not disturbed.
* We want to set an example, so others think twice about commiting heinous crimes, yet we don't televise or publisize executions. Heck, I am all for fishing or cutting bait. If we are going to be tough on crime and hope to scare the bejesus of future criminals by these harsh punishments, we should put them on evening news. You know, kids come home from school, everyone eats dinner, watch an execution (with frequent commercial breaks -- "Buy Tide! For a cleaner, fresher tomorrow"), and then everyone goes to bed.
* We say it is not about revenge and we use euphemisms like "justice" and "closure" instead, but it actually is about revenge.
It's theoretically more humane, and harder to screw up, to OD you on happy drugs. (It also looks more peaceful when one of those drugs is a paralytic.)
Oklahoma a few months ago introduced nitrogen asphyxiation as their backup plan. We know it's painless because a few people have accidentally entered nitrogen-heavy areas and didn't notice anything was wrong until they dropped unconscious (and were recovered before dying).