Great, very interesting article with compelling points. I went into reading it with the idea that I was going to counter your point, but your examples and ideas are spot on!
However, (attempting to play devils advocate), I would say that the only downside to this method of teaching math is that it squashes ANY chance at creativity. Math is already a subject with little room for individual creativity, and this method eliminates any chance at that. It shows the children that unless they do the problem EXACTLY the way the teacher wants, they are wrong. What does this do to kids as they get older? How are they going to solve the worlds problems if they are limited to only solving problems the way their bosses see fit? As you mentioned, it does have benefits (for CS and matrices), but looking at the larger picture, how valuable is creativity in this day and age?