If the only reason we sentence people to death were because it is more humane than putting them in prison for life, then it would be given as an option to the prisoner. I don't know of any case of someone sentenced to life in prison who argued they would rather be put to death.
Edit: I've now done some research and found some death-row-inmates do express a preference for a death sentence:
https://blogs.berkeley.edu/2012/09/25/why-death-row-inmates-...
https://www.quora.com/Is-prison-crueller-than-the-death-pena...
Criminals sentenced to death are supposed to be a danger to society so great that the only solution is to eliminate them. So, typical trolley problem: is it better to kill a criminal or let him go, potentially resulting in the death or several more innocent victims. Prison for life is another option, but is permanently restraining someone and endangering guards and other inmates a good alternative?
So yes, other justifications are needed. And the article gives one.