Because unironically, shooting him in the head would be infinitely cheaper, infinitely quicker, and infinitely more fun for the executioner than any other method save for hanging (except for the quicker part).
It’s also painless, the most expensive cost would be hiring someone to clean up afterwards.
Something else you have to keep in mind with people like this, we do not ask to be born into society, or as humans. Most of us enjoy who we are and love being a part of society for the most part, but killers often time do not feel human, they feel like it is the world and themselves, separate not the same. Whatever the case may be that causes this, including a condition or mental illness.
Yes, what has to be done must be done, but you should understand that it is not something that is done or should be done out of some kind of revenge hate fetish, it is something that is done to remove those people from our society because they are unfortunately too dangerous to be left alive, too dangerous to live even in a standard prison.
Once you start adding hate, anger, revenge, etc to the mix, you might as well just start throwing the zyklon b and burn pits in too, because that’s what a society that kills with hatred does. Unless that person has specifically done something to you, your family, or your friends, you should harbor no hatred for them, only sympathy.