As much as I dislike the idea of a government killing someone for a crime, the cost and potential elimination of future trouble with an individual is tempting.
Assuming that we absolutely know that someone is guilt (ignoring how that would happen), it doesn't need to take years and millions of dollars to simply shoot someone.
Then there are the people who are not only a financial burden on society, they are actively making it worse, much worse. Sometimes we just sit back an wonder why even spend resources keep this person terrible person imprisoned for decades. People who have killed, raped or tortured and been in and out of jail multiple times, no we really need to keep them around?
Regardless of how much we may hate the idea of the death penalty, there is some cold, brutal logic to simply shooting someone.