It's okay to laugh at the ancient Greek and its words that look similar to us, but we should not forget that the words with different accents sounded differently, so it was probably not confusing to native speakers. Moreover, every language has its homophonies (the English "Dick" is not just a first name), and many near-homophonies for strangers (Japanese untrained ears can't distinguish "r" from "l", and I can't identify "o" from "a" in most Russian words).
A nitpick about the article: a paragraph about the other main diacritics would have given more context. The breathing marks chang the pronunciation as much as the accents did. And since Roman languages are not tonal languages, they kept the breathing as a "h" but dropped the tones.