Short answer: No
Because first-degree murder constitutes a very serious crime, a conviction results in very serious punishment. In many states, a conviction for first-degree murder can result in the death penalty or life in prison without the possibility of parole.
Although the death penalty does not benefit society. It is often applied in a arbitrary and discriminatory manner. The methods of execution and death row conditions have been condemned as cruel, inhumane, or degrading treatment; possibly considered as torture. The death penalty has failed to protect the innocent, and had resulted in deaths of innocent people. If the death penalty were to be used on the wrong person, then that is irreversible.
The death penalty does not deter crime. States with the death penalty don’t have a lower crime rate than those without it. People commit murders with little to no thought of possible consequences to their acts. These people are often under the influence of substances or are mentally ill. Rather than punish these people, we could give them the help they need.