It's easy to find psychologically stable, trained professionals with experience shooting to kill.
-- "Shoot Me Now: Are firing squads a better means of execution than lethal injection?"
Interesting. Who are these people? The people who would have such experience would have it in contexts not quite on the same level as shooting an unarmed person in this context unless we are importing executioners from other countries or something. The military (and firing squads would be a logical execution technique in that place, especially if the execution had to be done "in the field") would be a logical place, but soldiers do not have much experience, do they, killing someone quite in this context. "Shooting to kill" changes when you kill an unarmed American like this.
An early ruling on the 8A concerned execution by firing squad in Utah. The technique has special significance there because of the idea of "blood atonement" and perhaps partially as a desire not to mistreat the body. See this story. This is interesting symbolism that might very well reflect beliefs of many who support the death penalty in some fashion. The importance of a "clean kill" is also reflected in the slaughter requirements of certain religions, which this would be an analogue. Is allowing it as an option here of First Amendment significance?!
Firing squads might seem to some to be uncivilized and/or out of date. As an opponent of the death penalty, I do find the argument against them as a means somewhat weak. The humane kill lethal injection model -- shades of putting little kitty to sleep I assume -- is problematic. If firing squads are not more painful (and methods like electrocution and gas has problems in that area in particular; lethal injection is not free from problems either), the main benefit appears to be to make us feel better. This separation from the event [those shooters are ultimately our agents] is not totally ideal and use of a 'medical' technique when involvement of medical personnel is unethical is problematic as well.*
If we are uncomfortable with the firing squad, it is likely largely because we are uncomfortable with carrying out the death penalty itself. Lethal injection allows us to separate ourselves from the process. It might be (marginally?) better in some ways, but in others, not so much.
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* The article linked at top cites various cases where lethal injection was problematic in practice, but the benefits of the firing squad on a pure "less pain" basis is open to question. One study cited suggests lethal injection might be better. Justice Stevens cited another in that opinion regarding use of the gas chamber. But, the firing squad is so rarely used and the limited value on the pain front is clouded by the other factors discussed.