Crimes heinous enough to currently be considered capital offenses are heinous enough to deserve the solo cell except for showers and solitary periods in a small exercise pen (wrists shackled together and to waist while being moved between cell and shower or exercise pen). Should have daytime lighting (no view of outdoors) and controlled
access to reading material and music.
While there are doubts the death penalty deters people who are not yet in prison, it certainly deters the condemed from killing prison staff and other inmates after the execution.
There's also the issue that offenders sentenced to life without the possibility parole don't have the risk of execution if they kill another inmate or a member of the prison staff.