Earlier quoted context omitted.
It can also, as my Japanese textbook pointed out, be faster to read if you're familiar with the characters in a body of text. Like the difference between reading "one hundred forty-three" vs "143". It's the input that kills you. But I think computer/smartphone semi-phonetic input kind of gets you the best of both worlds.
I'm skeptical of the "quick to read" argument. An educated Chinese speaker generally knows something in the neighborhood of 5,000 characters ("full literacy" is supposed to be 3k-4k), which is far less than readers of phonetic systems (20k-35k). Unless you're a professional writer of some variety you're going to spend more time looking up words in Chinese.
Especially in these 4 character groupings, you can find a lot of efficiency and elegance. It expresses ideas & meaning that would take 20-100 words to fully express.