Not exactly.

There are four reasons for the State to exact a penalty: justice, defense against the criminal, deterrence, rehabilitation, in that order of importance.

St. John Paul II first states "the primary purpose of the punishment which society inflicts is 'to redress the disorder caused by the offence'", and then discusses the second reason:

"If bloodless means are sufficient to defend human lives against an aggressor and to protect public order and the safety of persons, public authority must limit itself to such means."

So, if only the death penalty will be adequate to achieve justice, we need look no further.

As to defense against the criminal, there are nations such as Mexico where the criminals are so powerful, and the civil authority so weak, that - as  has been demonstrated repeatedly - imprisonment may be ineffective in defending against the criminal, who run their activities from their cells.