>Shorter words, yes. Convey information faster - only if you have perfect speakers and perfect listeners. Otherwise, in the best case you'd just have people ask - did you just say "hélló" or "hëllò"? In the worse case, they'd just misunderstand what you're saying. And since you strive to eliminate redundancy, instead of nonsense which would trigger request for repetition, you'd get meaning - but meaning something else that you didn't intend to say.
Perhaps I didn't include enough context from the document. He cited Esperanto as containing 34 phonemes, compared to English at 43, and then a list including Andean Spanish with 17, Japanese with 14, Hawai'ian with 8, or Rotokas with 6. That is, he cited (what seem to be) outliers with the smallest number of phonemes and implied that these were desirable. Later he notes that Eastern Polish has 49 phonemes.
I agree that a language can certainly have phonemes which are difficult to distinguish (Mandarin Chinese is famous for this) or hard to pronouce (the voiced "th" in English "the" is famous for this) or inscrutable for some listeners (most English speakers cannot distinguish dz from d), but I thought his minimalism was too extreme.