This is a reasonable stance, and I believe that it makes sense in your head, but I promise that if you try to actually write a law, "aren't true" and "damage others" are basically impossible to define. You're gonna have to draw some arbitrary-seeming lines based on how you want society to look, and be open to moving the lines if there are unexpected consequences. You can't write a clean protocol definition of acceptable human communication.

Would you pass a law that makes all lying illegal? Why not? Does speech have to directly damage someone? Financially, emotionally, what? What threshold of damage is punishable? Couldn't one argue that promoting communism "damages others"? The Secretary of Defense announcing a fake foreign invasion should probably be illegal, but a random drunk person claiming "the Chinese are invading" probably shouldn't be. So there's a line somewhere between those two people, where is it?