The article literally says:
> there is no "si" in the hiragana table, so s_ + (i) = shi. […] this is why it's important that you don't actually "think in" romaji. […] i'm using romaji as a convenient way to refer to phonetics in text. however, your "mental algebra" should match the hiragana table.
That’s just false, “si” is in the hiragana table as し. The romanization “si” is /si/ which is pronounced [ɕi] (or [ɕi̥] or some other possibility). This is basic Japanese phonetics.
If you fix all the errors that are in the article, at best there is an argument buried here that Hepburn romanization should not be used to teach Japanese to English speakers—but I think that point is really my own argument that I’m making with the fragments of the article that make sense.
Romanization can be more consistent with Japanese phonetics or it can be more consistent with English phonetics, and the Hepburn romanization is more consistent with English phonetics, which is why it’s a good choice for English speakers that don’t know Japanese, but a bad choice for English speakers who are trying to learn Japanese.