Lethal injection is more for the comfort of the people performing and watching the execution and to avoid the public outcry that more graphic methods would invariably provoke. If you paralyze the body, things look nice and peaceful even if the guy is somehow still awake and suffocating or having a fatal heart attack. It's even more likely to happen now that drug manufacturers are refusing to produce the old standbys and the executioners are basically having to experiment on the condemned.
It's probably more humane and certainly simpler to just execute the condemned with a gunshot to the back of the head or by a firing squad or guillotine. But it's a hell of a lot harder to perform or watch. But then perhaps that's not so bad. Maybe it should be a hard thing to do.
Like I said before, I generally think we overuse the death penalty. But people like Tsarnaev and McVeigh are a special case.
Settle in for a long wait.