First, As a basic part of Japanese language education, students are expected to be familiar with different romanization systems. If you ask a student where “si” is in the table, they should be able to find it. If a student says “it’s not in the table” then they’ve failed the lesson or there is something wrong with the teaching material.
Second: am I arguing that the choice of using Hepburn here is somehow bad? Yes, that’s correct. I think Hepburn is a bad choice here. A good choice is Nihon-shiki. JSL romanization is also fine.
Hepburn is the official romanization chosen by the Japanese government (it's a relatively recent change), kunrei-shiki has been deprecated and all the signs etc are in the process of being converted to Hepburn.
I've looked at over a dozen hiragana tables and they all use Hepburn romanization.
Obsessing over romanization, something that a student ought to outgrow, is a sure fire way for a student to get overwhelmed by irrelevant details that discourage learning. The hard part is putting in the work, not learning less than a dozen exceptions.
We’re talking about the same thing but you insist that there is only one angle under which things aren’t confusing. I disagree. That’s fine. The two systems are isomorphic, and I genuinely believe that, given I’ve described every single caveat of Hepburn in the article, I’ve paid my dues for using it. YMMV. I even include the “finding in the table” part.
I think I agree that Nihon-shiki and explaining it upfront would’ve made the article more elegant. One constraint I wanted to hit is that a person should be able to read this article with zero knowledge of Japanese, and walk away with being able to conjugate almost every verb to every suffix correctly. This is more of a challenge to myself as a writer than any practical need but hope it shed some light on the choices and the framing. I liked Hepburn because it’s closer to how it sounds. You can imagine I’m using IPA instead if you want.