> To me it is obvious that the method in the article is far superior than teaching completing the square.

I disagree. I would need some convincing that "two numbers that multiply to C and sum to B must have an average of B/2, so they must be B/2 + z and B/2 - z, so (B/2 + z)(B/2 - z) = C" is by any means obviously superior to completing the square. Neither is immediately intuitive; both will require prompting and teaching by the teacher. Completing the square has uses beyond proving the quadratic theorem; this does not.

I should say: I find this an incredibly cool and level-appropriate proof of the quadratic equation, but I think its merits as an improvement in pedagogy are dubious.