I don't know about healing the world, but psychedelics can for sure help humans to see reality as it truly is and not by biological programming.
Our survival programming is made to be practical and evolutionarily successful. This means that sometimes humans understand reality not by what it actually is, but by what is most practical.
Psychedelics can drastically change the perspective and reveal how things work.
With this information, the high-performance human is able to make more a more educated guess about how things are and what is the most appropriate course of action.
I like this article.