I'm not sure I understand. My knives are razor sharp (I keep a Shapton 1000 and 4000 on my counter along with a strop, my daily driver is a carbon steel I have to wipe down every time I cut a vegetable). They sail through the onion, but the sliced-up onion still splays out to both sides when I make the horizontal cut, and if you watch cooks doing it, it happens there too. What harm am I doing to the structure of the onion by doing it in the "wrong order"? They're the same cuts. The difference seems to be that in my order, the onion stays more stationary.

Don't get me wrong, I'm sure there's a reason everyone is doing it this way, because it's kind of clearly more annoying than the way I'm doing it?

(I'm just nerding out on this).

I still don't get why you need the horizontal cut at all. The diagram at the bottom of the blog post shows how unnecessary it is when you do the vertical cuts at a narrow range of angles like that (which I have been doing for a while now).