The death penalty only fully works if it is automatic. Not up to a jury or judge. Rather once he’s convicted of murder the sentence is automatically death. The court should only decide upon guilt or innocence, not upon the sentence.
Even Texas only executes a tiny portion of their murderers. If all 50 states automatically executed every convicted murderer (upon the exhaustion of his appeals, which itself must be done swiftly) the murder rate in the United States would drop percipitously. This has never occurred yet since the death penalty has only been applied selectively.
That said, the death penalty should be applied for reasons of justice, not merely determent.
Rav Moshe zt’l petitioned New York State Governor Mario Cuomo to reinstate the death penalty in New York. It is in the Igros Moshe.