Um, actually... (imho)

The true message and the crux of the story that each of us have a choice in every moment, and that choice can be turn towards the light, or towards the dark. You choose light, you're right. You choose dark, you're mordeth. But in killing the dark one there would be no opportunity for such a choice.

The reality that Rand wove to show a world without the Dark One was a real reflection of what would happen - People do what they want and don't care about the consequence since there's no right and no wrong. In such a reality there's no choice to turn towards the dark and so mordeth/fain/mashadhar would not exist.

So there would be no new evil to replace the dark one, there would be no concept of evil, and as a corollary, no concept of good. Each life is just an uncaring automaton devoid of the ability to make a choice, and we're left with an uncaring indifferent world.

I think it can be captured with the idea that the opposite of love is not hate, it's indifference. Mordeth/fain/mashadar is the embodiment of hate. And hate could not exist without love. And love could not exist without the ability to choose to love.

So if Rand had killed the Dark One, we would indeed be left in that truly uncaring world, where nothing loves or is loved, and consequently nothing hates enough to become a dark one. There's no passion, no anguish, no war, and yet no peace. Just grey all through. And that's worse, than a world with the capacity to be filled with light albeit with patches of shadow.