I think that's where your proposal breaks down. Light is powerhungry and arrogant, but he's also very moralistic. A character that proritizes fear over accuracy would be a different character than Light. He wants to build a better, even perfect, world. And for that, he must have accuracy. Otherwise he's a mere tyrant, something he believes he is not.
Of course, it's worth saying, the great archetypal tragedy of the story, and what makes it excellent literature, is that his goal is unacheivable. Humans are deeply imperfect and powerless to end evil completely. And the process of trying turns us into the worst of all monsters that can possibly exist.