You make some good points. The U.S. has the highest incarceration rate in the world. So clearly, incarceration is not a deterrent to crime.
When you say the "only" justification is anger, hate, etc." I have to disagree. People that commit horrific crimes such as murder, should, and in many cases do, forfeit their right to remain in society at large. However, I believe the thought behind execution is not only for the safety of the population at large but also it's the ultimate justice, an eye for eye.
I'm not sure I understand your reference to religious indoctrination, speaking only for the U.S., which is largely christian, the death penalty is widely disparaged and is already not used in nearly half the states based on moral concerns. Is this what you mean by religious indoctrination?
In case of absolute proof of guilt, I have no problem with the death penalty. It serves no purpose to incarcerate a person until they die. That is, in itself, a certain sort of death in my opinion. Some years ago large portions of the U.S. prison system were privatized and now run as a business. I wonder how much this affects the incarceration rate, if at all? Perhaps it's good business for the prisons to have lifetime "customers".
And, to your point about gun control, I agree 100%. Based on the mass shootings, the daily shootings, and general violence around our gun culture I have to wonder why a certain faction of our government steadfastly refuses to implement some safety measures. In fact, that contingent is steadily working to make gun access easier. Several southern states have done away with the need for any sort of training to get a concealed carry permit and anyone in those states over (18?), can carry a concealed gun. Moreover, many states allow open carry. Much like the wild west, one can strap a gun in their holster and head out to the grocery store. It's very difficult to fathom.