As someone intimately familiar with this topic, the article here is mostly correct but gets a lot of the small details wrong. Probably the most important missing part here is the reason non-Hepburn systems like Kunrei stuck around for so long: they were designed to replace the Japanese script completely. This sounds outlandish today, but they were invented during the early Meiji years when Japan was adopting Western…
What surprises me (only a little) is that Japan continues to use Chinese characters when they've got a perfectly good native syllabary.
I don't know if this is from the perspective of having learned Mandarin in elementary school first or if Japanese folks feel similarly, but reading words like, e.g., だいがくいんせい versus 大学院生 is actually a little more annoying because I have to scan more of the line to read the word in question. This is notwithstanding the effect that hiragana has in highlighting grammatical structures; it's a lot like setting off Finnish case endings and verb conjugations in a different color.
At least, that's the reason why I prefer still having kanji around.