I get what you’re saying, it’s certainly a hard situation, and a rare one, but I think “truly nothing we can do” is an exceptionally rare situation.
But why is that person acting the way they are? People do things for reasons, even if they aren’t good ones. Maybe the only way they can safely interact with people is via video chat, and respecting the humanity of the others around them means that’s all they get. There are ways for them to get access to food, water, shelter, sunlight, even socialization, without physical access to others, and access to somebody to talk to who might be able to help them, even if the DSM doesn’t have a specific diagnosis that describes them.
I think any system that deals with people who have done what society has labelled crime should seek to minimize harm, and maximize opportunities to grow for those who wish to take them. I don’t think your “textbook” case for the death penalty achieves either of these aims.