Why? Because he believes that if the "Remnants of Despair" (his friends) are all executed, their deaths will create the most magnificent, shining hope in history.
In the final chapters of the game, after Nagito’s death, Hajime carries the weight of that loss. He doesn’t mention Nagito in a eulogy. He internalizes the brutal lesson: Hope without empathy is just another form of despair. Losing A Forbidden Flower Nagito