I have an intense dislike of EM. My eldest was spared as the school started on EM with the class below her. Middle kid didn't think it was so bad, but she just "gets" math. Little one had it last year, but might only have one more year if she scores well on her placement tests.

I agree that no one does simple problems by writing them out. But as kids get a bit more advanced, they are expected to write out answers. How about this problem:

http://www.artofproblemsolving.com/Wiki/index.php/2014_AIME_II_Problems/Problem_9

While you could just write down the math for the problem without explanation, it would not be easy for someone else to follow your thinking. As a civil engineer, I don't just write down the math, but include a bit of explanation as it would be tough to sort through all kinds of calculations for a very large site without some written explanation.

While I think I know what the teacher means, most kids will never need to write out explanations like that. Or they won't need to do that for many years, and can be taught when they are older.