That's a really good point. Though I do think the article is specifically about math, it generalizes to the point you're making.
I thought the article did a particularly good job explaining how the "new math" is very dependent on high quality teaching rather than adhering to a new curriculum.
Unfortunately, I think this is where the US has fallen down where it comes to math (and, as you've pointed out, other subjects). We seem to think we need to find the magic approach that will work.
My kids are in school, and they are doing common core math. In many ways I do think it's much better than the old way (put the big number in the house, put the little number outside the house... except if you're dividing the little number by the big number...). There are a lot of good ways to add fractions, or do long division. It's not only math, but math is actually an unusually good subject to teach this kind of creative problem solving.
Here's what I see as the problem: we observe a teacher approaching a problem a different way. When students are asked to subtract 4 3/4 from 6 2/5, you could do the ol' algorithmic cross multiply trick. It's long, and boring, but it does work. Or, you could write the numbers down on a number line, notice that there are distances between the numbers that amount to integers, and small additional bits of remaining distances that amount to fractions. Add those up and you've got your solution.
That's just one of many possible approaches. My guess is that a talented teacher might do this, or something else.
Here's what I feel common core does: it notices one particular creative approach and concludes, "oh, the way to teach this is Step 1: create a number line, step 2: mark off the whole numbers, Step 3:..."
Essentially, they're looking to reduce the creative approach to another mechanical set of steps. This may be an overstatement and overuse of this phrase, but it's sort of a "cargo cult" of math instruction. The point never was the number line, it was that a teacher was talented enough to see a better approach for this problem, and that, after repeated examples and exercises, the students develop this ability as well.
I do think this article gets at this - that the point isn't the particular "creative" approach, it's the creative approach itself.
Unfortunately, this will never work without talented teachers. They need to be drawn from the top tier of math grads, they need to be very good at teaching and connecting with students, they need to be fluid and creative in their approach, and they need excellent training and experience.
Almost nothing about the US educational system, outside a few very selective and rare programs, would draw this sort of person into teaching (I hope it's obvious I'm not talking about research universities).
The irony is, once you have these teachers, I suspect don't really need to formalize this approach! "Common Core Math", if done well, is probably what talented, creative math teachers would naturally do on their own. You can't get it from a set of mechanical steps, and if you're doing what you should (drawing in top teachers), you don't need the mechanical steps anyway.