> Sometimes, even if someone is sentenced to life in prison they are let out and kill again.

Life without parole exists

> Also, putting remorseless killers in prison also represents a threat to other prisoners. We haven't figured out how to prevent that yet.

Solitary confinement exists

> Should capital punishment be more strictly controlled with a massively high barrier to use, yes, but there are solid reasons to use it.

What are the solid reasons to kill somebody in prison ?