It doesn't appear to me that the problem with the death penalty in the States is because of a particular obsession with violence. The same probably goes for the stuff about guns.

Both those things are much more to do with politics and constitutional arrangements.

Most people in the UK are also in favour of the death penalty, as is the case in the USA. A different political structure here meant that this fact didn't stop it being abolished. I'm grateful for that. Majorities aren't the only thing that matters.

Again, from what I've read, a majority in the USA would actually favour stricter gun controls. What stops that happening is a particular interpretation of a clause in a Constitution written a couple of centuries ago. The same reason the death penalty is still in operation (different clause, same Constitution.)

In time there'll very likely be a Supreme Court that decides that a different interpretation of the Constitution means that "the right to bear arms" should be interpreted in a much more restrictive sense". And very likely it'll also decide that the death penalty is a "cruel and unusual punishment", and so outlawed by the Constitution.

If/when that happens that won't mean that generalisations about how violent America is are any less invalid, or any more valid than they are today.