You can pick nits off of that nit, too. Korean can use a mix of phonetic writing and Chinese characters, just like Japanese does. Its usage is dwindling rapidly, but people writing software arguably still have to be prepared to handle this kind of text.
I recall opening some book in Korean pertaining to linguistics: almost every words had its hanja version in-between parenthesis. This was quite ridiculous: the mixed-script version would have been almost twice shorter, and the content was not understandable without hanja anyway.
Every language (without notable secondary dialects) with a recently defined orthographic system is "simpler" because its orthography seamlessly matches its phonetic structure. Give it another few hundred years of phonetic drift -- especially combined with dialect profusion -- and you'll find that this "beautifully simple" orthographic system is every bit as warty as English's is.
Just remember, there is an old enough English (dialect) where "knight" is pronounced "keh - nih - ch - t": where the orthography perfectly matches the pronunciation. It's just not any of the spoken dialects of modern English.
It is said that "a wise man can acquaint himself with them before the morning is over; even a stupid man can learn them in the space of ten days."
So I think the acronym "CJK" is just a geographic grouping, not a linguistic one.