And since it's so brain dead to implement, I can't see any significant amount of kids even reflecting on how 'the numbers work' based on that.
FWIW, I routinely find people who can't do simple single-times-double digit multiplications in their head, simply because it never occurs to them that they can turn 7 * 12 into (7 * 10) + (7 * 2), or 7 * 3 (=21) * 4 (4x2=8,4x1=4, =84). I figured out how to do so myself, school never taught it to me, and I seriously doubt more than a 5% left my high school knowing how to do this, much less actually using it.
I'm not sure that I would leap to calling it retarded. I agree that it takes up more paper but paper isn't the most expensive thing in the world.
What it does do is make explicit why the old school method works. Look at the explanation given by the article for the old method:
'Answer = 720, Because: 2x36 = 72, with a 0 added in the ones place.'
No, the reason you get 720 isn't because you 'added' a 0 in the ones place (72+0 = 72). It's because you are multiplying by 20 and not by 2. The old method hides this fact and corrects for it by a mechanical process: first write down a zero and then shift the other entries to the left.
Your criticism is analogous to calling Assembly retarded because Haskell exists. They serve different purposes.