I'm not intelligent enough to understand what an optimal strategy for the survival of mankind would consist of. However, not having a death sentence guarantees taxpayers the following things for their money.
They will not get executed from being falsely sentenced, meaning they can likely return to a regular life eventually. Or at least find something else to dedicate their lives to in prison. No accusation is a threat so serious it could completely destroy a person's life by chance.
Dictatorships will have a tougher time emerging. Executing active non-believers is an effective way of directly limiting the spread of opposing ideas. Doing so also quiets the remaining political opponents through fear, further keeping opinions of anything but the greatness of the glorious dictatorship from prevailing.
These non-aggressive but politically dangerous people will be named criminals by the ruling party. Sometimes excecuted for being "a threat to the society", and the few who manage to have original opinions after all the information control and want to argue with that can step in the execution line also; other times through completely forged accusitions that few doubt because all the media is party controlled.
It is highly beneficial to a dictator to have a legal way to sentence their opponents to death. However, if a country has banned the death sentence the wanna be dictating party would first have to make executions legal again. That would give time for the dictatorship opposing part of the nation to predict the emerge, react, and throw the party out of the game.
So having no death sentence serves the people as a level of proof against being executed for political reasons in the future. And against being ruled for a long time by a goverment who excelled in mind control over management abilities, a goverment who is likely to bring down the quality of life in the nation. thus resulting