That's an interesting perspective to take. Those countries in Europe who have prohibited capital punishment have done so because we believe it is immoral even in the case of absolute certainty of guilt. Take Anders Breivik for example: there is no doubt whatsoever of his guilt - he is a mass murderer. Nevertheless, according to modern European concepts of morality he should be treated well even in prison, and the Norwegians take that to a level that many other countries would find absurd.
When we decline to execute a heinous offender, and decline to treat them as inhuman - even when they have offended inhumanly - it demonstrates the moral difference between us and them.
Does Anders truly "win" by being simply in confinement forever, rather than being dead? What does he gain? His life? What life? Playing PS1 games forever, seeing the same four walls forever, acceptable but certainly not impressive meals forever. There is not a single thing anyone can do to him or anyone else to undo what he did, and causing him suffering certainly doesn't bring back any children. More importantly, killing him does not make any of the damage he caused go away.
Americans love to piss and moan about all the freedoms we supposedly have, but are conspicuously unsatisfied with merely removing said freedoms as punishment for crimes.
Maybe they don't think "freedom" is that important or meaningful
There is continued harm though. Every day he is treated well, every day he gets food and shelter and care is food and shelter and care paid for by you, that could have been spent on others.
"Those countries in Europe" is perhaps a bit of an understatement. Any justice system that practices capital punishment is considered so dysfunctional that any plans on joining the European Union is out of the question. This is also why the system is rigged as to make it impossible to extradite someone if there is even the slightest possibility of a death penalty.
Breivik is also a single person; do you really want to change (or even burn down) the entire system just for one person?
In principle I have no trouble just executing Breivik; his guilt is established beyond doubt, he committed an act of exceptional evil, and he more or less declares to want to do it again (well technically he says he wants to be a "non-violent Nazi" or some such, but that's a contradiction in terms: "oh that Holocaust thing was just brilliant, more of that!" is violent rhetoric).
But Breivik-type case are rare. So rare it's not really worth changing the system over it. There's principle of a thing and the practicalities of it: in principle the death penalty is fine, but practically organizing that in a legal system with zero false positives is very difficult, so it's not really worth it.
Aside from the US, you can also look at post-second world war in Europe, which saw some executions that were rather over the top in hindsight.
If you spend some time in the Nordics, you'd find that most don't think "death penalty is fine in principle" as it goes against many of the principles people there try to live by.
He's not treated well. Maybe compared other (inhuman) places, but he feels his treatment is so vindictive that he has tried getting the human rights court involved.
His protests as well as the treatment often perceived as "absurdly comfortable" all hinge on one fact: he is kept in permanent solitary confinement. Which is otherwise considered an additional (and harsh) punishment for regular prisoners. And it's the reason why he has his private gym and entertainment facilities, because those would normale be available as shared facilities to regular prisoners.
https://en.wikipedia.org/wiki/Anders_Behring_Breivik