Oh, duh, binary. NM. 
And would you believe people tell me I’m highly intelligent? 
More generally, K/[2^(N)*(5^M)] has two decimal representations, one that ends with infinite 0s and one that ends with infinite 9s. You want the diagonal to be properly formed (the first) one.
Few people ever remember “use only properly-formed representations in the original list.” But yes, you can do that.
The beauty of the proof is its sheer simplicity for such a complex and innovative concept. Why add the unnecessary to it?
This is a fairly simple example of mathematical pedagogy at American universities.
I doubt any but a small fraction of US high school teachers would ever touch the CDA.
Intro Real Analysis at the uni is the most common introduction, I’d guess almost everywhere in the country. The class is about the reals. So the CDA is used for the reals. I haven’t personally heard a professor ever not mention the .999… thing. I likewise doubt any commonly-used textbook textbook misses it or makes any other error. (But you never know.)
So practically any student who needs Intro Real Analysis but not much beyond that (so not mathematicians, but scientists or economists or whoever) is likely to have encountered it only one time, using the reals only, and is going to think of it that way.
If they’re sharing it, they are unlikely to be as rigorous as their professor. That might be the source of your exposure.
This is just completely baked-in at this point. The CDA is used for real analysis because that is where it’s used.
The set theory in such a class is cursory introduction, not the main point of the thing. Cantor’s Theorem is “here it is, this goes interesting places, now back to the reals”.