In fact, I'd argue the opposite. The French system places a big emphasis on learning grammar, conjugations, spelling and things like that - which frankly is a waste of time. I don't think I ever took a grammar course in the US. I couldn't tell you what a prepositional phrase is, but I can write a good essay.
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.
Sure you get better at things you actually enjoy doing, but sometimes you need to force yourself or - in the case of children - be forced to do something over and over to learn. I think teachers try to make writing more interesting, but it can be a pretty hard thing to do. Most kids will hate it no matter what they write.
Writing, perhaps, but not good writing. Most of good writing is the ability to synthesize ideas and construct prose people want to read.
Nobody wants to read your average student's five paragraph essay. On the other hand, I spent a large part of the weekend bingeing on Michael O. Church's blog, because the dude can write.