Just to give a first person example of what others have already said:
I was in an unschool-at-school type situation, and I HATED to write. Loathed it. Journal time came, when we could write anything at all, and all I would write is "I hate writing. I hate writing. I hate writing. Writing is stupid. Why do I have to do this? This is stupid. I hate writing." Only, well, not that well written.
That was all I would have to do with writing, until I was about 11. When I wrote a poem. And another one. And I was, y'know, for an 11 year old, pretty good at it.
So I would write, for the next couple years, stories and poems and that was about it.
When I got to highschool (normal California public education, ugh!), they started asking for "proto essays," and then "essays," and I complained and moaned, and did it totally half-heartedly. And I was way better than anyone else in my class. And eventually I found out that not only was I good at it, but I liked it. (Not the school stuff, usually, but every once in a while, there'd be a topic I'd like. Those are the assignments I actually turned in...)
And now I'm a writer. My handwriting is absolutely atrocious, but so's my brother's, who went to "normal" school, and so are both my parents', and so were all of my grandparents', so I'm pretty sure I couldn't have escaped it if I tried. (Although I did spend most of Junior year writing the alphabet only about a million times, when I was supposed to be taking notes, in an attempt to go improve to atrocious - before that it was simply illegible.) But I'm a writer; essays flow from me like breath. I got scholarships to college simply for my writing. I could no more give up the written word than I could give up food. It may not be my main profession, but it will always be a large part of who I am, and what is important to have in my life.
So the moral of the story is to trust your kids. They will get there, if they want to! And if not, there's not a lot of point trying to force them. Essay style, like grammer, isn't something they need to have taught to them using metacommunication ("This is a paragraph. Essays have three types of paragraphs. Here are the three types of essay paragraphs." Blech!). It comes out of the desire to communicate, or to persuade, or to entertain. Anyone can learn, in about five minutes, what an "essay" is. In one easy sentence: say what you're going to say, say it, then say what you said. Do you think your kid can't learn that in a snap when she's ready to? Far more important than that is to learn what it is she wants to say. That takes a lot longer.
At least 11 years!