I can write a good essay, too, but I don't really attribute that to my schooling. Learning to write a good essay has one essential ingredient: you have to care about what you're trying to express. If you're just writing to the specification, you won't improve at anything except creating filler content.

I learned how to write a good essay because I thought I had something to say and I wanted people to hear it and understand it. Same with other facets of communication, like public speaking.